## [Maxima-commits] CVS: maxima/tests rtest14.mac,1.64,1.65

 [Maxima-commits] CVS: maxima/tests rtest14.mac,1.64,1.65 From: Dieter Kaiser - 2009-09-25 18:38:33 ```Update of /cvsroot/maxima/maxima/tests In directory 23jxhf1.ch3.sourceforge.com:/tmp/cvs-serv2956/tests Modified Files: rtest14.mac Log Message: Updating some examples. Now the function assoc_legendre_q simplifies. Index: rtest14.mac =================================================================== RCS file: /cvsroot/maxima/maxima/tests/rtest14.mac,v retrieving revision 1.64 retrieving revision 1.65 diff -u -d -r1.64 -r1.65 --- rtest14.mac 19 Sep 2009 23:28:10 -0000 1.64 +++ rtest14.mac 25 Sep 2009 18:38:21 -0000 1.65 @@ -545,7 +545,7 @@ * * */ -ratsimp(specint( t^(3/2)*bessel_y(1,a*t)*%e^(-t),t)); +ratsimp(specint(t^(3/2)*bessel_y(1,a*t)*%e^(-t),t)); ''(ratsimp(15*%i*(1/(a^2+1)-1)^(3/4)*(1/(sqrt(a^2+1)+1)^(3/2)+1/(1-sqrt(a^2+1))^(3/2))/ (16*sqrt(a^2+1)))) \$ @@ -807,9 +807,15 @@ * This simplifies to log((1+p/r)/a) = log(p/a+sqrt(1+(p/a)^2)) = asinh(p/a). * * So we have -2/%pi/sqrt(p^2+a^2)*asinh(p/a). + * + * With revision 1.64 of hypgeo.lisp we simplify the Legendre Q function. + * The result is equivalent to the above formula. */ specint(bessel_y(0,a*t)*exp(-p*t),t); --2/%pi/sqrt(p^2+a^2)*legendre_q(0,p/sqrt(p^2+a^2)) \$ + +/*-2/%pi/sqrt(p^2+a^2)*legendre_q(0,p/sqrt(p^2+a^2)) \$*/ + + -log((sqrt(p^2+a^2)+p)/(sqrt(p^2+a^2)-p))/(%pi*sqrt(p^2+a^2)); /* * (46) @@ -830,9 +836,14 @@ * -2/%pi/(p^2+a^2)*(p/r*log((p+r)/a) - 1) * * = 2/%pi/(p^2+a^2)*(1-p/sqrt(p^2+a^2)*log((p+sqrt(p^2+a^2))/a)) + * + * The Legendre Q function simplifes accordingly. */ -specint(t*bessel_y(0,a*t)*exp(-p*t),t); --2/%pi/(p^2+a^2)*legendre_q(1,p/sqrt(p^2+a^2)) \$ +factor(specint(t*bessel_y(0,a*t)*exp(-p*t),t)); +/*-2/%pi/(p^2+a^2)*legendre_q(1,p/sqrt(p^2+a^2)) \$*/ + +(p*log((sqrt(p^2+a^2)+p)/(sqrt(p^2+a^2)-p))-2*sqrt(p^2+a^2)) + /(-%pi*(p^2+a^2)^(3/2)); /* * (47) @@ -863,8 +874,12 @@ * as expected. * */ -specint(t*bessel_y(1,a*t)*exp(-p*t),t); --4/%pi/(p^2+a^2)*assoc_legendre_q(1,-1,p/sqrt(p^2+a^2))\$ +factor(specint(t*bessel_y(1,a*t)*exp(-p*t),t)); +/*-4/%pi/(p^2+a^2)*assoc_legendre_q(1,-1,p/sqrt(p^2+a^2))\$*/ + +(a^2*log((sqrt(p^2+a^2)+p)/(sqrt(p^2+a^2)-p))+2*p*sqrt(p^2+a^2)) + /(%pi*a*(p^2+a^2)^(3/2)); + /* * Some tests for step7 ```

 [Maxima-commits] CVS: maxima/tests rtest14.mac,1.64,1.65 From: Dieter Kaiser - 2009-09-25 18:38:33 ```Update of /cvsroot/maxima/maxima/tests In directory 23jxhf1.ch3.sourceforge.com:/tmp/cvs-serv2956/tests Modified Files: rtest14.mac Log Message: Updating some examples. Now the function assoc_legendre_q simplifies. Index: rtest14.mac =================================================================== RCS file: /cvsroot/maxima/maxima/tests/rtest14.mac,v retrieving revision 1.64 retrieving revision 1.65 diff -u -d -r1.64 -r1.65 --- rtest14.mac 19 Sep 2009 23:28:10 -0000 1.64 +++ rtest14.mac 25 Sep 2009 18:38:21 -0000 1.65 @@ -545,7 +545,7 @@ * * */ -ratsimp(specint( t^(3/2)*bessel_y(1,a*t)*%e^(-t),t)); +ratsimp(specint(t^(3/2)*bessel_y(1,a*t)*%e^(-t),t)); ''(ratsimp(15*%i*(1/(a^2+1)-1)^(3/4)*(1/(sqrt(a^2+1)+1)^(3/2)+1/(1-sqrt(a^2+1))^(3/2))/ (16*sqrt(a^2+1)))) \$ @@ -807,9 +807,15 @@ * This simplifies to log((1+p/r)/a) = log(p/a+sqrt(1+(p/a)^2)) = asinh(p/a). * * So we have -2/%pi/sqrt(p^2+a^2)*asinh(p/a). + * + * With revision 1.64 of hypgeo.lisp we simplify the Legendre Q function. + * The result is equivalent to the above formula. */ specint(bessel_y(0,a*t)*exp(-p*t),t); --2/%pi/sqrt(p^2+a^2)*legendre_q(0,p/sqrt(p^2+a^2)) \$ + +/*-2/%pi/sqrt(p^2+a^2)*legendre_q(0,p/sqrt(p^2+a^2)) \$*/ + + -log((sqrt(p^2+a^2)+p)/(sqrt(p^2+a^2)-p))/(%pi*sqrt(p^2+a^2)); /* * (46) @@ -830,9 +836,14 @@ * -2/%pi/(p^2+a^2)*(p/r*log((p+r)/a) - 1) * * = 2/%pi/(p^2+a^2)*(1-p/sqrt(p^2+a^2)*log((p+sqrt(p^2+a^2))/a)) + * + * The Legendre Q function simplifes accordingly. */ -specint(t*bessel_y(0,a*t)*exp(-p*t),t); --2/%pi/(p^2+a^2)*legendre_q(1,p/sqrt(p^2+a^2)) \$ +factor(specint(t*bessel_y(0,a*t)*exp(-p*t),t)); +/*-2/%pi/(p^2+a^2)*legendre_q(1,p/sqrt(p^2+a^2)) \$*/ + +(p*log((sqrt(p^2+a^2)+p)/(sqrt(p^2+a^2)-p))-2*sqrt(p^2+a^2)) + /(-%pi*(p^2+a^2)^(3/2)); /* * (47) @@ -863,8 +874,12 @@ * as expected. * */ -specint(t*bessel_y(1,a*t)*exp(-p*t),t); --4/%pi/(p^2+a^2)*assoc_legendre_q(1,-1,p/sqrt(p^2+a^2))\$ +factor(specint(t*bessel_y(1,a*t)*exp(-p*t),t)); +/*-4/%pi/(p^2+a^2)*assoc_legendre_q(1,-1,p/sqrt(p^2+a^2))\$*/ + +(a^2*log((sqrt(p^2+a^2)+p)/(sqrt(p^2+a^2)-p))+2*p*sqrt(p^2+a^2)) + /(%pi*a*(p^2+a^2)^(3/2)); + /* * Some tests for step7 ```