;;; -*- Mode: Lisp; package:maxima; syntax:common-lisp ;Base: 10 -*- ;;; (in-package "MAXIMA") ;;** Variable settings were ** ;;TRANSCOMPILE:TRUE; ;;TR_SEMICOMPILE:FALSE; ;;TRANSLATE_FAST_ARRAYS:TRUE; ;;TR_WARN_UNDECLARED:COMPILE; ;;TR_WARN_MEVAL:COMPFILE; ;;TR_WARN_FEXPR:COMPFILE; ;;TR_WARN_MODE:ALL; ;;TR_WARN_UNDEFINED_VARIABLE:ALL; ;;TR_FUNCTION_CALL_DEFAULT:GENERAL; ;;TR_ARRAY_AS_REF:TRUE; ;;TR_NUMER:FALSE; ;;DEFINE_VARIABLE:FALSE; (SIMPLIFY (MFUNCTION-CALL $PUT '|$specfun| 110 '$VERSION)) (PROGN (DEFPROP |$floor_rat| T TRANSLATED) (ADD2LNC '|$floor_rat| $PROPS) (DEFMTRFUN (|$floor_rat| $ANY MDEFINE NIL NIL) (|$m| |$n|) (DECLARE (SPECIAL |$n| |$m|) (FIXNUM |$n| |$m|)) ((LAMBDA () NIL NIL (SIMPLIFY ($FIRST (SIMPLIFY (MFUNCTION-CALL $DIVIDE |$m| |$n|)))))))) (EVAL-WHEN (LOAD) (SETQ $FLOAT2BF T)) (PROGN (DEFPROP |$float_bfloatp| T TRANSLATED) (ADD2LNC '|$float_bfloatp| $PROPS) (DEFMTRFUN (|$float_bfloatp| $BOOLEAN MDEFINE NIL NIL) (|$x|) (DECLARE (SPECIAL |$x|)) ((LAMBDA () NIL (OR (MFUNCTION-CALL $FLOATNUMP |$x|) (MFUNCTION-CALL $BFLOATP |$x|)))))) (PROGN (DEFPROP |$complex_floatp| T TRANSLATED) (ADD2LNC '|$complex_floatp| $PROPS) (DEFMTRFUN (|$complex_floatp| $BOOLEAN MDEFINE NIL NIL) (|$x|) (DECLARE (SPECIAL |$x|)) ((LAMBDA () NIL (COND ((MFUNCTION-CALL $ATOM |$x|) NIL) (T (AND (MFUNCTION-CALL $CONSTANTP |$x|) (MFUNCTION-CALL |$float_bfloatp| (SIMPLIFY (MFUNCTION-CALL $REALPART |$x|))) (MFUNCTION-CALL |$float_bfloatp| (SIMPLIFY (MFUNCTION-CALL $IMAGPART |$x|)))))))))) (PROGN (DEFPROP |$floating_pointp| T TRANSLATED) (ADD2LNC '|$floating_pointp| $PROPS) (DEFMTRFUN (|$floating_pointp| $BOOLEAN MDEFINE NIL NIL) (|$x|) (DECLARE (SPECIAL |$x|)) ((LAMBDA () NIL (OR (MFUNCTION-CALL |$float_bfloatp| |$x|) (MFUNCTION-CALL |$complex_floatp| |$x|)))))) (PROGN (DEFPROP |$coerce_return_type| T TRANSLATED) (ADD2LNC '|$coerce_return_type| $PROPS) (DEFMTRFUN (|$coerce_return_type| $ANY MDEFINE NIL NIL) (|$x| |$y|) (DECLARE (SPECIAL |$y| |$x|)) ((LAMBDA ($RATPRINT) (DECLARE (SPECIAL $RATPRINT)) (COND ((MFUNCTION-CALL $FLOATNUMP |$x|) ($FLOAT |$y|)) ((MFUNCTION-CALL $BFLOATP |$x|) (SIMPLIFY (MFUNCTION-CALL $BFLOAT |$y|))) ((MFUNCTION-CALL |$complex_floatp| |$x|) (SIMPLIFY (MFUNCTION-CALL $EXPAND |$y|))) (T |$y|))) NIL))) (PROGN (DEFPROP |$jacobi_p| T TRANSLATED) (ADD2LNC '|$jacobi_p| $PROPS) (DEFMTRFUN (|$jacobi_p| $ANY MDEFINE NIL NIL) (|$n| |$a| |$b| |$x|) (DECLARE (SPECIAL |$x| |$b| |$a| |$n|)) ((LAMBDA (|$sofar| |$w| |$abn| |$m| |$s_args|) (DECLARE (SPECIAL |$s_args| |$m| |$abn| |$w| |$sofar|) (FIXNUM |$m|)) NIL (COND ((AND (MFUNCTION-CALL $INTEGERP |$n|) (IS-BOOLE-CHECK (MGRP |$n| -1)) (OR (NOT (MFUNCTION-CALL $INTEGERP |$a|)) (IS-BOOLE-CHECK (MGRP |$a| -1))) (OR (NOT (MFUNCTION-CALL $INTEGERP |$b|)) (IS-BOOLE-CHECK (MGRP |$b| -1)))) (COND ((AND (IS-BOOLE-CHECK (SIMPLIFY (MAPPLY-TR '|&and| (SIMPLIFY (MAP1 (GETOPR '$CONSTANTP) (LIST '(MLIST) |$a| |$b| |$x|)))))) (IS-BOOLE-CHECK (SIMPLIFY (MAPPLY-TR '|&and| (SIMPLIFY (MAP1 (GETOPR '$FLOATNUMP) (LIST '(MLIST) |$a| |$b| |$x|))))))) (SIMPLIFY (MFUNCTION-CALL |$jacobi_pf| |$n| ($FLOAT |$a|) ($FLOAT |$b|) ($FLOAT |$x|)))) (T (SETQ |$sofar| 1) (SETQ |$w| 1) (SETQ |$x| (DIV (ADD* |$x| -1) 2)) (SETQ |$abn| (ADD* |$a| |$b| |$n|)) (DO ((|$m| 1 (F+ 1 |$m|))) ((IS-BOOLE-CHECK (MGRP |$m| |$n|)) '$DONE) (SETQ |$w| (DIV (MUL* |$w| (ADD* |$n| 1 (- |$m|)) (ADD* |$abn| |$m|) |$x|) (MUL* |$m| (ADD* |$a| |$m|)))) (SETQ |$sofar| (ADD* |$sofar| |$w|))) (SIMPLIFY (MFUNCTION-CALL |$coerce_return_type| |$x| (MUL* (SIMPLIFY (LIST '(%BINOMIAL) (ADD* |$n| |$a|) |$n|)) |$sofar|)))))) ((IS-BOOLE-CHECK (SIMPLIFY (MFUNCTION-CALL $FEATUREP |$n| '$INTEGER))) (SETQ |$s_args| (LIST '(MLIST) (MUL* (SIMPLIFY (LIST '(%BINOMIAL) (ADD* |$n| |$a|) '|$m|)) (SIMPLIFY (LIST '(%BINOMIAL) (ADD* |$n| |$b|) (ADD* |$n| (*MMINUS '|$m|)))) (POWER (ADD* |$x| -1) (ADD* |$n| (*MMINUS '|$m|))) (POWER (ADD* |$x| 1) '|$m|)) '|$m| 1 (ADD* |$n| -1))) (DIV (ADD* (MUL* (SIMPLIFY (LIST '(%BINOMIAL) (ADD* |$n| |$a|) 0)) (SIMPLIFY (LIST '(%BINOMIAL) (ADD* |$n| |$b|) |$n|)) (POWER (ADD* |$x| -1) |$n|)) (MUL* (SIMPLIFY (LIST '(%BINOMIAL) (ADD* |$n| |$a|) |$n|)) (SIMPLIFY (LIST '(%BINOMIAL) (ADD* |$n| |$b|) 0)) (POWER (ADD* |$x| 1) |$n|)) (SIMPLIFY (MAPPLY-TR '$SUM |$s_args|))) (POWER 2 |$n|))) (T (SIMPLIFY (MFUNCTION-CALL $FUNMAKE '|$jacobi_p| (LIST '(MLIST) |$n| |$a| |$b| |$x|)))))) '|$sofar| '|$w| '|$abn| 0 '((MLIST))))) (MEVAL '(($GRADEF) ((|$jacobi_p|) |$n| |$a| |$b| |$x|) ((%DERIVATIVE) ((|%jacobi_p|) |$n| |$a| |$b| |$x|) |$n|) ((%DERIVATIVE) ((|%jacobi_p|) |$n| |$a| |$b| |$x|) |$a|) ((%DERIVATIVE) ((|%jacobi_p|) |$n| |$a| |$b| |$x|) |$b|) ((MQUOTIENT) ((MPLUS) ((MTIMES) |$n| ((MPLUS) |$a| ((MMINUS) |$b|) ((MTIMES) ((MMINUS) ((MPLUS) ((MTIMES) 2 |$n|) |$a| |$b|)) |$x|)) ((|%jacobi_p|) |$n| |$a| |$b| |$x|)) ((MTIMES) 2 ((MPLUS) |$n| |$a|) ((MPLUS) |$n| |$b|) ((|%jacobi_p|) ((MPLUS) |$n| ((MMINUS) 1)) |$a| |$b| |$x|))) ((MTIMES) ((MPLUS) ((MTIMES) 2 |$n|) |$a| |$b|) ((MPLUS) 1 ((MMINUS) ((MEXPT) |$x| 2))))))) (PROGN (DEFPROP |$jacobi_pf| T TRANSLATED) (ADD2LNC '|$jacobi_pf| $PROPS) (DEFMTRFUN (|$jacobi_pf| $ANY MDEFINE NIL NIL) (|$n| |$a| |$b| |$x|) (DECLARE (SPECIAL |$x| |$b| |$a| |$n|) (FLONUM |$x| |$b| |$a|) (FIXNUM |$n|)) ((LAMBDA (|$sofar| |$w| |$abn| |$np1| |$m|) (DECLARE (SPECIAL |$m| |$np1| |$abn| |$w| |$sofar|) (FLONUM |$np1| |$abn| |$w| |$sofar|) (FIXNUM |$m|)) NIL (SETQ |$sofar| 1.0) (SETQ |$w| 1.0) (SETQ |$x| (//$ (+$ |$x| -1.0) 2.0)) (SETQ |$abn| (+$ |$a| |$b| (FLOAT |$n|))) (SETQ |$np1| (+$ 1.0 (FLOAT |$n|))) (DO ((|$m| 1 (F+ 1 |$m|))) ((> |$m| |$n|) '$DONE) (SETQ |$w| (//$ (*$ |$w| (+$ |$np1| (FLOAT (- |$m|))) (+$ |$abn| (FLOAT |$m|)) |$x|) (*$ (FLOAT |$m|) (+$ |$a| (FLOAT |$m|))))) (SETQ |$sofar| (+$ |$sofar| |$w|))) (MUL* (SIMPLIFY (LIST '(%BINOMIAL) (+$ (FLOAT |$n|) |$a|) |$n|)) |$sofar|)) 0.0 0.0 0.0 0.0 0))) (PROGN (DEFPROP |$ultraspherical| T TRANSLATED) (ADD2LNC '|$ultraspherical| $PROPS) (DEFMTRFUN (|$ultraspherical| $ANY MDEFINE NIL NIL) (|$n| |$a| |$x|) (DECLARE (SPECIAL |$x| |$a| |$n|)) ((LAMBDA () NIL NIL (DIV (MUL* (SIMPLIFY (LIST '(%GAMMA) (ADD* |$a| (RREMAINDER 1 2)))) (SIMPLIFY (LIST '(%GAMMA) (ADD* (MUL* 2 |$a|) |$n|))) (SIMPLIFY (MFUNCTION-CALL |$jacobi_p| |$n| (ADD* |$a| (RTIMES -1 (RREMAINDER 1 2))) (ADD* |$a| (RTIMES -1 (RREMAINDER 1 2))) |$x|))) (MUL* (SIMPLIFY (LIST '(%GAMMA) (MUL* 2 |$a|))) (SIMPLIFY (LIST '(%GAMMA) (ADD* |$a| |$n| (RREMAINDER 1 2)))))))))) (PROGN (DEFPROP |$assoc_legendre_p| T TRANSLATED) (ADD2LNC '|$assoc_legendre_p| $PROPS) (DEFMTRFUN (|$assoc_legendre_p| $ANY MDEFINE NIL NIL) (|$n| |$m| |$x|) (DECLARE (SPECIAL |$x| |$m| |$n|)) ((LAMBDA (|$c|) (DECLARE (SPECIAL |$c|)) NIL (COND ((AND (MFUNCTION-CALL $INTEGERP |$n|) (MFUNCTION-CALL $INTEGERP |$m|) (IS-BOOLE-CHECK (MGRP |$n| -1))) (COND ((IS-BOOLE-CHECK (MGRP (SIMPLIFY (LIST '(MABS) |$m|)) |$n|)) 0) ((IS-BOOLE-CHECK (MLSP |$m| 0)) (DIV (MUL* (SIMPLIFY (LIST '(%GAMMA) (ADD* |$n| (*MMINUS |$m|) 1))) (SIMPLIFY (MFUNCTION-CALL |$assoc_legendre_p| |$n| (*MMINUS |$m|) |$x|))) (SIMPLIFY (LIST '(%GAMMA) (ADD* |$n| |$m| 1))))) (T (COND ((LIKE |$m| 0) (SETQ |$c| 1)) (T (SETQ |$c| (SIMPLIFY (LIST '(%GENFACT) (ADD* (MUL* 2 |$m|) -1) (ADD* |$m| -1) 2))))) (MUL* |$c| (POWER -1 |$m|) (POWER (ADD* 1 (*MMINUS (POWER |$x| 2))) (DIV |$m| 2)) (SIMPLIFY (MFUNCTION-CALL |$ultraspherical| (ADD* |$n| (*MMINUS |$m|)) (ADD* |$m| (RREMAINDER 1 2)) |$x|)))))) (T (SIMPLIFY (MFUNCTION-CALL $FUNMAKE '|$assoc_legendre_p| (LIST '(MLIST) |$n| |$m| |$x|)))))) '|$c|))) (MEVAL '(($GRADEF) ((|$assoc_legendre_p|) |$n| |$m| |$x|) ((%DERIVATIVE) ((|%assoc_legendre_p|) |$m| |$m| |$x|) |$n|) ((%DERIVATIVE) ((|%alegendre_p|) |$n| |$m| |$x|) |$m|) ((MQUOTIENT) ((MPLUS) ((MTIMES) |$n| |$x| ((|%assoc_legendre_p|) |$n| |$m| |$x|)) ((MMINUS) ((MTIMES) ((MPLUS) |$n| |$m|) ((|%assoc_legendre_p|) ((MPLUS) |$n| ((MMINUS) 1)) |$m| |$x|)))) ((MPLUS) ((MEXPT) |$x| 2) ((MMINUS) 1))))) (PROGN (DEFPROP |$legendre_q| T TRANSLATED) (ADD2LNC '|$legendre_q| $PROPS) (DEFMTRFUN (|$legendre_q| $ANY MDEFINE NIL NIL) (|$n| |$x|) (DECLARE (SPECIAL |$x| |$n|)) ((LAMBDA (|$m| |$leg_p| |$sofar| $RATPRINT) (DECLARE (SPECIAL $RATPRINT |$sofar| |$leg_p| |$m|) (FIXNUM |$m|)) NIL (COND ((AND (MFUNCTION-CALL $INTEGERP |$n|) (IS-BOOLE-CHECK (MGRP |$n| -1))) (SETQ |$leg_p| '((MLIST))) (DO ((|$m| 0 (F+ 1 |$m|))) ((IS-BOOLE-CHECK (MGRP |$m| |$n|)) '$DONE) (SETQ |$leg_p| (SIMPLIFY (MFUNCTION-CALL $ENDCONS (SIMPLIFY (MFUNCTION-CALL |$legendre_p| |$m| |$x|)) |$leg_p|)))) (SETQ |$sofar| 0) (DO ((|$m| 1 (F+ 1 |$m|))) ((IS-BOOLE-CHECK (MGRP |$m| |$n|)) '$DONE) (SETQ |$sofar| (ADD* |$sofar| (DIV (MUL* (SIMPLIFY (MFUNCTION-CALL $PART |$leg_p| |$m|)) (SIMPLIFY (MFUNCTION-CALL $PART |$leg_p| (ADD* |$n| (- |$m|) 1)))) |$m|)))) (ADD* (DIV (MUL* (SIMPLIFY (MFUNCTION-CALL $PART |$leg_p| (ADD* |$n| 1))) (SIMPLIFY (LIST '(%LOG) (DIV (ADD* 1 |$x|) (ADD* 1 (*MMINUS |$x|)))))) 2) (*MMINUS |$sofar|))) (T (SIMPLIFY (MFUNCTION-CALL $FUNMAKE '|$legendre_q| (LIST '(MLIST) |$n| |$x|)))))) 0 '((MLIST)) '|$sofar| NIL))) (PROGN (DEFPROP |$assoc_legendre_q| T TRANSLATED) (ADD2LNC '|$assoc_legendre_q| $PROPS) (DEFMTRFUN (|$assoc_legendre_q| $ANY MDEFINE NIL NIL) (|$n| |$m| |$x|) (DECLARE (SPECIAL |$x| |$m| |$n|)) ((LAMBDA (|$x%| |$f| $RATPRINT) (DECLARE (SPECIAL $RATPRINT |$f| |$x%|)) NIL (COND ((AND (MFUNCTION-CALL $INTEGERP |$n|) (IS-BOOLE-CHECK (MGRP |$n| -1)) (MFUNCTION-CALL $INTEGERP |$m|)) (COND ((IS-BOOLE-CHECK (MLSP |$m| 0)) (DIV (MUL* (POWER -1 |$m|) (SIMPLIFY (LIST '(MFACTORIAL) (ADD* |$n| |$m|))) (SIMPLIFY (MFUNCTION-CALL |$assoc_legendre_q| |$n| (*MMINUS |$m|) |$x|))) (SIMPLIFY (LIST '(MFACTORIAL) (ADD* |$n| (*MMINUS |$m|)))))) (T (SETQ |$f| (SIMPLIFY (MFUNCTION-CALL $RATSIMP (MUL* (POWER -1 |$m|) (POWER (ADD* 1 (*MMINUS (POWER |$x| 2))) (DIV |$m| 2)) (SIMPLIFY (MFUNCTION-CALL $DIFF (SIMPLIFY (MFUNCTION-CALL |$legendre_q| |$n| |$x%|)) |$x%| |$m|)))))) (SIMPLIFY (MFUNCTION-CALL $SUBSTITUTE |$x| |$x%| |$f|))))) (T (SIMPLIFY (MFUNCTION-CALL $FUNMAKE '|$assoc_legendre_q| (LIST '(MLIST) |$n| |$m| |$x|)))))) '|$x%| '|$f| NIL))) (PROGN (DEFPROP |$chebyshev_t| T TRANSLATED) (ADD2LNC '|$chebyshev_t| $PROPS) (DEFMTRFUN (|$chebyshev_t| $ANY MDEFINE NIL NIL) (|$n| |$x|) (DECLARE (SPECIAL |$x| |$n|)) ((LAMBDA () NIL NIL (COND ((OR (AND (MFUNCTION-CALL $INTEGERP |$n|) (IS-BOOLE-CHECK (MGRP |$n| -1))) (IS-BOOLE-CHECK (SIMPLIFY (MFUNCTION-CALL $FEATUREP |$n| '$INTEGER)))) (DIV (MUL* (SIMPLIFY (LIST '(MFACTORIAL) |$n|)) (POWER 2 |$n|) (SIMPLIFY (MFUNCTION-CALL |$jacobi_p| |$n| (RREMAINDER -1 2) (RREMAINDER -1 2) |$x|))) (SIMPLIFY (LIST '(%GENFACT) (ADD* (MUL* 2 |$n|) -1) |$n| 2)))) (T (SIMPLIFY (MFUNCTION-CALL $FUNMAKE '|$chebyshev_t| (LIST '(MLIST) |$n| |$x|))))))))) (MEVAL '(($GRADEF) ((|$chebyshev_t|) |$n| |$x|) ((%DERIVATIVE) ((|%chebyshev_t|) |$n| |$x|) |$n|) ((MQUOTIENT) ((MPLUS) ((MTIMES) ((MMINUS) |$n|) |$x| ((|%chebyshev_t|) |$n| |$x|)) ((MTIMES) |$n| ((|%chebyshev_t|) ((MPLUS) |$n| ((MMINUS) 1)) |$x|))) ((MPLUS) 1 ((MMINUS) ((MEXPT) |$x| 2)))))) (PROGN (DEFPROP |$chebyshev_u| T TRANSLATED) (ADD2LNC '|$chebyshev_u| $PROPS) (DEFMTRFUN (|$chebyshev_u| $ANY MDEFINE NIL NIL) (|$n| |$x|) (DECLARE (SPECIAL |$x| |$n|)) ((LAMBDA () NIL NIL (COND ((OR (AND (MFUNCTION-CALL $INTEGERP |$n|) (IS-BOOLE-CHECK (MGRP |$n| -1))) (IS-BOOLE-CHECK (SIMPLIFY (MFUNCTION-CALL $FEATUREP |$n| '$INTEGER)))) (DIV (MUL* (SIMPLIFY (LIST '(MFACTORIAL) (ADD* |$n| 1))) (POWER 2 |$n|) (SIMPLIFY (MFUNCTION-CALL |$jacobi_p| |$n| (RREMAINDER 1 2) (RREMAINDER 1 2) |$x|))) (SIMPLIFY (LIST '(%GENFACT) (ADD* (MUL* 2 |$n|) 1) (ADD* |$n| 1) 2)))) (T (SIMPLIFY (MFUNCTION-CALL $FUNMAKE '|$chebyshev_u| (LIST '(MLIST) |$n| |$x|))))))))) (MEVAL '(($GRADEF) ((|$chebyshev_u|) |$n| |$x|) ((%DERIVATIVE) ((|%chebyshev_u|) |$n| |$x|) |$n|) ((MQUOTIENT) ((MPLUS) ((MTIMES) ((MMINUS) |$n|) |$x| ((|%chebyshev_u|) |$n| |$x|)) ((MTIMES) ((MPLUS) |$n| 1) ((|%chebyshev_u|) ((MPLUS) |$n| ((MMINUS) 1)) |$x|))) ((MPLUS) 1 ((MMINUS) ((MEXPT) |$x| 2)))))) (PROGN (DEFPROP |$laguerre| T TRANSLATED) (ADD2LNC '|$laguerre| $PROPS) (DEFMTRFUN (|$laguerre| $ANY MDEFINE NIL NIL) (|$n| |$x|) (DECLARE (SPECIAL |$x| |$n|)) ((LAMBDA ($RATPRINT) (DECLARE (SPECIAL $RATPRINT)) NIL (SIMPLIFY (MFUNCTION-CALL |$gen_laguerre| |$n| 0 |$x|))) NIL))) (PROGN (DEFPROP |$gen_laguerre| T TRANSLATED) (ADD2LNC '|$gen_laguerre| $PROPS) (DEFMTRFUN (|$gen_laguerre| $ANY MDEFINE NIL NIL) (|$n| |$a| |$x|) (DECLARE (SPECIAL |$x| |$a| |$n|)) ((LAMBDA (|$sofar| |$w| |$m| $RATPRINT) (DECLARE (SPECIAL $RATPRINT |$m| |$w| |$sofar|) (FIXNUM |$m|)) NIL (COND ((AND (MFUNCTION-CALL $INTEGERP |$n|) (IS-BOOLE-CHECK (MGRP |$n| -1))) (SETQ |$sofar| 1) (SETQ |$w| 1) (DO ((|$m| 1 (F+ 1 |$m|))) ((IS-BOOLE-CHECK (MGRP |$m| |$n|)) '$DONE) (SETQ |$w| (DIV (MUL* (*MMINUS |$w|) |$x| (ADD* |$n| (- |$m|) 1)) (MUL* |$m| (ADD* |$m| |$a|)))) (SETQ |$sofar| (ADD* |$sofar| |$w|))) (SIMPLIFY (MFUNCTION-CALL |$coerce_return_type| |$x| (MUL* (SIMPLIFY (LIST '(%BINOMIAL) (ADD* |$n| |$a|) |$n|)) |$sofar|)))) (T (SIMPLIFY (MFUNCTION-CALL $FUNMAKE '|$gen_laguerre| (LIST '(MLIST) |$n| |$a| |$x|)))))) '|$sofar| '|$w| 0 NIL))) (MEVAL '(($GRADEF) ((|$gen_laguerre|) |$n| |$a| |$x|) ((%DERIVATIVE) ((|%gen_laguerre|) |$n| |$a| |$x|) |$n|) ((%DERIVATIVE) ((|$gen_laguerre|) |$n| |$a| |$x|) |$a|) ((MQUOTIENT) ((MPLUS) ((MTIMES) |$n| ((|$gen_laguerre|) |$n| |$a| |$x|)) ((MMINUS) ((MTIMES) ((MPLUS) |$n| |$a|) ((|$gen_laguerre|) ((MPLUS) |$n| ((MMINUS) 1)) |$a| |$x|)))) |$x|))) (PROGN (DEFPROP |$legendre_p| T TRANSLATED) (ADD2LNC '|$legendre_p| $PROPS) (DEFMTRFUN (|$legendre_p| $ANY MDEFINE NIL NIL) (|$n| |$x|) (DECLARE (SPECIAL |$x| |$n|)) ((LAMBDA () NIL NIL (COND ((OR (AND (MFUNCTION-CALL $INTEGERP |$n|) (IS-BOOLE-CHECK (MGRP |$n| -1))) (IS-BOOLE-CHECK (SIMPLIFY (MFUNCTION-CALL $FEATUREP |$n| '$INTEGER)))) (SIMPLIFY (MFUNCTION-CALL |$jacobi_p| |$n| 0 0 |$x|))) (T (SIMPLIFY (MFUNCTION-CALL $FUNMAKE '|$legendre_p| (LIST '(MLIST) |$n| |$x|))))))))) (MEVAL '(($GRADEF) ((|$legendre_p|) |$n| |$x|) ((%DERIVATIVE) ((|%legendre_p|) |$n| |$x|) |$n|) ((MQUOTIENT) ((MPLUS) ((MTIMES) ((MMINUS) |$n|) |$x| ((|$legendre_p|) |$n| |$x|)) ((MTIMES) |$n| ((|$legendre_p|) ((MPLUS) |$n| ((MMINUS) 1)) |$x|))) ((MPLUS) 1 ((MMINUS) ((MEXPT) |$x| 2)))))) (PROGN (DEFPROP |$hermite| T TRANSLATED) (ADD2LNC '|$hermite| $PROPS) (DEFMTRFUN (|$hermite| $ANY MDEFINE NIL NIL) (|$n| |$x|) (DECLARE (SPECIAL |$x| |$n|)) ((LAMBDA () NIL NIL (COND ((MFUNCTION-CALL $INTEGERP |$n|) (COND ((MFUNCTION-CALL $EVENP |$n|) (SETQ |$n| (MFUNCTION-CALL |$floor_rat| |$n| 2)) (SIMPLIFY (MFUNCTION-CALL |$coerce_return_type| |$x| (MUL* (POWER -1 |$n|) (POWER 4 |$n|) (SIMPLIFY (LIST '(MFACTORIAL) |$n|)) (SIMPLIFY (MFUNCTION-CALL |$gen_laguerre| |$n| (RREMAINDER -1 2) (POWER |$x| 2))))))) (T (SETQ |$n| (MFUNCTION-CALL |$floor_rat| |$n| 2)) (SIMPLIFY (MFUNCTION-CALL |$coerce_return_type| |$x| (MUL* (POWER -1 |$n|) (POWER 2 (ADD* (MUL* 2 |$n|) 1)) (SIMPLIFY (LIST '(MFACTORIAL) |$n|)) |$x| (SIMPLIFY (MFUNCTION-CALL |$gen_laguerre| |$n| (RREMAINDER 1 2) (POWER |$x| 2))))))))) (T (SIMPLIFY (MFUNCTION-CALL $FUNMAKE '|$hermite| (LIST '(MLIST) |$n| |$x|))))))))) (MEVAL '(($GRADEF) ((|$hermite|) |$n| |$x|) ((%DERIVATIVE) ((|%hermite|) |$n| |$x|) |$n|) ((MTIMES) 2 |$n| ((|$hermite|) ((MPLUS) |$n| ((MMINUS) 1)) |$x|)))) (PROGN (DEFPROP |$spherical_hankel2| T TRANSLATED) (ADD2LNC '|$spherical_hankel2| $PROPS) (DEFMTRFUN (|$spherical_hankel2| $ANY MDEFINE NIL NIL) (|$n| |$x|) (DECLARE (SPECIAL |$x| |$n|)) ((LAMBDA (|$sofar| |$w| |$m|) (DECLARE (SPECIAL |$m| |$w| |$sofar|) (FIXNUM |$m|)) NIL (COND ((MFUNCTION-CALL $INTEGERP |$n|) (COND ((IS-BOOLE-CHECK (MGRP |$n| -1)) (SETQ |$sofar| 1) (SETQ |$w| 1) (DO ((|$m| 0 (F+ 1 |$m|))) ((IS-BOOLE-CHECK (MGRP |$m| |$n|)) '$DONE) (SETQ |$w| (DIV (MUL* |$w| (ADD* |$n| |$m| 1) (ADD* |$n| (- |$m|))) (MUL* 2 '$%I |$x| (F+ |$m| 1)))) (SETQ |$sofar| (ADD* |$sofar| |$w|))) (SETQ |$sofar| (DIV (MUL* (POWER '$%I (ADD* |$n| 1)) (SIMPLIFY ($EXP (MUL* (*MMINUS '$%I) |$x|))) |$sofar|) |$x|)) (SIMPLIFY (MFUNCTION-CALL |$coerce_return_type| |$x| |$sofar|))) (T (MUL* '$%I (POWER -1 |$n|) (SIMPLIFY (MFUNCTION-CALL |$spherical_hankel2| (ADD* (*MMINUS |$n|) -1) |$x|)))))) (T (SIMPLIFY (MFUNCTION-CALL $FUNMAKE '|$spherical_hankel2| (LIST '(MLIST) |$n| |$x|)))))) '|$sofar| '|$w| 0))) (PROGN (DEFPROP |$spherical_hankel1| T TRANSLATED) (ADD2LNC '|$spherical_hankel1| $PROPS) (DEFMTRFUN (|$spherical_hankel1| $ANY MDEFINE NIL NIL) (|$n| |$x|) (DECLARE (SPECIAL |$x| |$n|)) (MUL* (POWER -1 |$n|) (SIMPLIFY (MFUNCTION-CALL |$spherical_hankel2| |$n| (*MMINUS |$x|)))))) (PROGN (DEFPROP |$p_fun| T TRANSLATED) (ADD2LNC '|$p_fun| $PROPS) (DEFMTRFUN (|$p_fun| $ANY MDEFINE NIL NIL) (|$n| |$x|) (DECLARE (SPECIAL |$x| |$n|) (FIXNUM |$n|)) ((LAMBDA (|$sofar| |$w| |$n1| |$m|) (DECLARE (SPECIAL |$m| |$n1| |$w| |$sofar|) (FIXNUM |$m| |$n1|)) NIL (SETQ |$sofar| 1) (SETQ |$w| 1) (SETQ |$n1| (F+ (MFUNCTION-CALL |$floor_rat| |$n| 2) -1)) (DO ((|$m| 0 (F+ 1 |$m|))) ((> |$m| |$n1|) '$DONE) (SETQ |$w| (DIV (MUL* (*MMINUS |$w|) (F+ |$n| (F* 2 |$m|) 2) (F+ |$n| (F* 2 |$m|) 1) (F+ |$n| (- (F* 2 |$m|))) (F+ |$n| (- (F* 2 |$m|)) -1)) (MUL* 4 (F+ (F* 2 |$m|) 1) (F+ (F* 2 |$m|) 2) (POWER |$x| 2)))) (SETQ |$sofar| (ADD* |$sofar| |$w|))) |$sofar|) '|$sofar| '|$w| 0 0))) (PROGN (DEFPROP |$q_fun| T TRANSLATED) (ADD2LNC '|$q_fun| $PROPS) (DEFMTRFUN (|$q_fun| $ANY MDEFINE NIL NIL) (|$n| |$x|) (DECLARE (SPECIAL |$x| |$n|) (FIXNUM |$n|)) ((LAMBDA (|$sofar| |$w| |$n1| |$m|) (DECLARE (SPECIAL |$m| |$n1| |$w| |$sofar|) (FIXNUM |$m| |$n1|)) NIL (COND ((EQL |$n| 0) 0) (T (SETQ |$sofar| 1) (SETQ |$w| 1) (SETQ |$n1| (F+ (MFUNCTION-CALL |$floor_rat| (F+ |$n| -1) 2) -1)) (DO ((|$m| 0 (F+ 1 |$m|))) ((> |$m| |$n1|) '$DONE) (SETQ |$w| (DIV (MUL* (*MMINUS |$w|) (F+ |$n| (F* 2 |$m|) 3) (F+ |$n| (F* 2 |$m|) 2) (F+ |$n| (- (F* 2 |$m|)) -1) (F+ |$n| (- (F* 2 |$m|)) -2)) (MUL* 4 (F+ (F* 2 |$m|) 3) (F+ (F* 2 |$m|) 2) (POWER |$x| 2)))) (SETQ |$sofar| (ADD* |$sofar| |$w|))) (DIV (MUL* (FACTORIAL (F+ |$n| 1)) |$sofar|) (MUL* 2 |$x| (FACTORIAL (F+ |$n| -1))))))) '|$sofar| '|$w| 0 0))) (PROGN (DEFPROP |$spherical_bessel_j| T TRANSLATED) (ADD2LNC '|$spherical_bessel_j| $PROPS) (DEFMTRFUN (|$spherical_bessel_j| $ANY MDEFINE NIL NIL) (|$n| |$x|) (DECLARE (SPECIAL |$x| |$n|)) ((LAMBDA () NIL NIL (COND ((MFUNCTION-CALL $INTEGERP |$n|) (COND ((IS-BOOLE-CHECK (MGRP |$n| -1)) (DIV (ADD* (MUL* (SIMPLIFY (MFUNCTION-CALL |$p_fun| |$n| |$x|)) (SIMPLIFY (LIST '(%SIN) (ADD* |$x| (*MMINUS (DIV (MUL* |$n| '$%PI) 2)))))) (MUL* (SIMPLIFY (MFUNCTION-CALL |$q_fun| |$n| |$x|)) (SIMPLIFY (LIST '(%COS) (ADD* |$x| (*MMINUS (DIV (MUL* |$n| '$%PI) 2))))))) |$x|)) (T (MUL* (POWER -1 |$n|) (SIMPLIFY (MFUNCTION-CALL |$spherical_bessel_y| (ADD* (*MMINUS |$n|) -1) |$x|)))))) (T (SIMPLIFY (MFUNCTION-CALL $FUNMAKE '|$spherical_bessel_j| (LIST '(MLIST) |$n| |$x|))))))))) (PROGN (DEFPROP |$spherical_bessel_y| T TRANSLATED) (ADD2LNC '|$spherical_bessel_y| $PROPS) (DEFMTRFUN (|$spherical_bessel_y| $ANY MDEFINE NIL NIL) (|$n| |$x|) (DECLARE (SPECIAL |$x| |$n|)) ((LAMBDA () NIL NIL (COND ((MFUNCTION-CALL $INTEGERP |$n|) (COND ((IS-BOOLE-CHECK (MGRP |$n| -1)) (DIV (MUL* (POWER -1 (ADD* |$n| 1)) (ADD* (MUL* (SIMPLIFY (MFUNCTION-CALL |$p_fun| |$n| |$x|)) (SIMPLIFY (LIST '(%COS) (ADD* |$x| (DIV (MUL* |$n| '$%PI) 2))))) (*MMINUS (MUL* (SIMPLIFY (MFUNCTION-CALL |$q_fun| |$n| |$x|)) (SIMPLIFY (LIST '(%SIN) (ADD* |$x| (DIV (MUL* |$n| '$%PI) 2)))))))) |$x|)) (T (MUL* (POWER -1 (ADD* |$n| 1)) (SIMPLIFY (MFUNCTION-CALL |$spherical_bessel_j| (ADD* (*MMINUS |$n|) -1) |$x|)))))) (T (SIMPLIFY (MFUNCTION-CALL $FUNMAKE '|$spherical_bessel_y| (LIST '(MLIST) |$n| |$x|))))))))) (MEVAL '(($GRADEF) ((|%spherical_hankel2|) |$n| |$x|) ((%DERIVATIVE) ((|%spherical_hankel2|) |$n| |$x|) |$n|) ((MQUOTIENT) ((MPLUS) ((MTIMES) |$n| ((|$spherical_hankel2|) ((MPLUS) |$n| ((MMINUS) 1)) |$x|)) ((MMINUS) ((MTIMES) ((MPLUS) |$n| 1) ((|$spherical_hankel2|) ((MPLUS) |$n| 1) |$x|)))) ((MPLUS) ((MTIMES) 2 |$n|) 1)))) (MEVAL '(($GRADEF) ((|%spherical_hankel1|) |$n| |$x|) ((%DERIVATIVE) ((|%spherical_hankel1|) |$n| |$x|) |$n|) ((MQUOTIENT) ((MPLUS) ((MTIMES) |$n| ((|$spherical_hankel1|) ((MPLUS) |$n| ((MMINUS) 1)) |$x|)) ((MMINUS) ((MTIMES) ((MPLUS) |$n| 1) ((|$spherical_hankel1|) ((MPLUS) |$n| 1) |$x|)))) ((MPLUS) ((MTIMES) 2 |$n|) 1)))) (MEVAL '(($GRADEF) ((|%spherical_bessel_j|) |$n| |$x|) ((%DERIVATIVE) ((|%spherical_bessel_j|) |$n| |$x|) |$n|) ((MQUOTIENT) ((MPLUS) ((MTIMES) |$n| ((|$spherical_bessel_j|) ((MPLUS) |$n| ((MMINUS) 1)) |$x|)) ((MMINUS) ((MTIMES) ((MPLUS) |$n| 1) ((|$spherical_bessel_j|) ((MPLUS) |$n| 1) |$x|)))) ((MPLUS) ((MTIMES) 2 |$n|) 1)))) (MEVAL '(($GRADEF) ((|%spherical_bessel_y|) |$n| |$x|) ((%DERIVATIVE) ((|%spherical_bessel_y|) |$n| |$x|) |$n|) ((MQUOTIENT) ((MPLUS) ((MTIMES) |$n| ((|$spherical_bessel_y|) ((MPLUS) |$n| ((MMINUS) 1)) |$x|)) ((MMINUS) ((MTIMES) ((MPLUS) |$n| 1) ((|$spherical_bessel_y|) ((MPLUS) |$n| 1) |$x|)))) ((MPLUS) ((MTIMES) 2 |$n|) 1)))) (PROGN (DEFPROP |$assoc_leg_cos| T TRANSLATED) (ADD2LNC '|$assoc_leg_cos| $PROPS) (DEFMTRFUN (|$assoc_leg_cos| $ANY MDEFINE NIL NIL) (|$n| |$m| |$x|) (DECLARE (SPECIAL |$x| |$m| |$n|) (FIXNUM |$m| |$n|)) ((LAMBDA (|$c|) (DECLARE (SPECIAL |$c|)) NIL (COND ((EQL |$m| 0) (SETQ |$c| 1)) (T (SETQ |$c| (SIMPLIFY (MFUNCTION-CALL $GENFACT (F+ (F* 2 |$m|) -1) (RREMAINDER (F+ (F* 2 |$m|) -1) 2) 2))))) (MUL* |$c| (POWER (SIMPLIFY (LIST '(%SIN) |$x|)) |$m|) (SIMPLIFY (MFUNCTION-CALL |$ultraspherical| (F+ |$n| (- |$m|)) (ADD* |$m| (RREMAINDER 1 2)) (SIMPLIFY (LIST '(%COS) |$x|)))))) '|$c|))) (PROGN (DEFPROP |$spherical_harmonic| T TRANSLATED) (ADD2LNC '|$spherical_harmonic| $PROPS) (DEFMTRFUN (|$spherical_harmonic| $ANY MDEFINE NIL NIL) (|$n| |$m| |$theta| |$phi|) (DECLARE (SPECIAL |$phi| |$theta| |$m| |$n|)) ((LAMBDA () NIL NIL (COND ((AND (MFUNCTION-CALL $INTEGERP |$n|) (MFUNCTION-CALL $INTEGERP |$m|) (IS-BOOLE-CHECK (MGRP |$n| -1)) (NOT (IS-BOOLE-CHECK (MGRP |$m| |$n|)))) (COND ((IS-BOOLE-CHECK (MLSP |$m| 0)) (MUL* (POWER -1 |$m|) (SIMPLIFY (MFUNCTION-CALL |$spherical_harmonic| |$n| (*MMINUS |$m|) |$theta| (*MMINUS |$phi|))))) (T (RATF (MUL* (SIMPLIFY ($EXP (MUL* '$%I |$m| |$phi|))) (SIMPLIFY (LIST '(%SQRT) (DIV (MUL* (ADD* (MUL* 2 |$n|) 1) (SIMPLIFY (LIST '(MFACTORIAL) (ADD* |$n| (*MMINUS |$m|))))) (MUL* 4 '$%PI (SIMPLIFY (LIST '(MFACTORIAL) (ADD* |$n| |$m|))))))) (SIMPLIFY (MFUNCTION-CALL |$assoc_leg_cos| |$n| |$m| |$theta|))))))) (T (SIMPLIFY (MFUNCTION-CALL $FUNMAKE '|$spherical_harmonic| (LIST '(MLIST) |$n| |$m| |$theta| |$phi|))))))))) (MEVAL '(($GRADEF) ((|$spherical_harmonic|) |$n| |$m| |$theta| |$phi|) ((%DERIVATIVE) ((|$spherical_harmonic|) |$n| |$m| |$theta| |$phi|) |$n|) ((%DERIVATIVE) ((|$spherical_harmonic|) |$n| |$m| |$theta| |$phi|) |$m|) ((MPLUS) ((MQUOTIENT) ((MTIMES) ((MMINUS) ((%SQRT) ((MTIMES) ((MPLUS) |$n| ((MMINUS) |$m|)) ((MPLUS) |$n| |$m| 1)))) (($EXP) ((MTIMES) ((MMINUS) $%I) |$phi|)) ((|$spherical_harmonic|) |$n| ((MPLUS) |$m| 1) |$theta| |$phi|)) 2) ((MQUOTIENT) ((MTIMES) ((%SQRT) ((MTIMES) ((MPLUS) |$n| |$m|) ((MPLUS) |$n| ((MMINUS) |$m|) 1))) (($EXP) ((MTIMES) $%I |$phi|)) ((|$spherical_harmonic|) |$n| ((MPLUS) |$m| ((MMINUS) 1)) |$theta| |$phi|)) 2)) ((MTIMES) $%I |$m| ((|$spherical_harmonic|) |$n| |$m| |$theta| |$phi|))))