I am working on several problems that involve infinite sums, and the expressions can get quite complicated. Sage can solve some of these, such as
m,p = var('m,p') #taylor coefficient for erf(3x) a_erf(m) = (3)^(2*m+1)*(-1)^m*2/sqrt(pi)/(factorial(m)*(2*m+1)) #coefficient of chebyshev polynomial c_erf_cheb(p) = sum(a_erf(m)*binomial(2*m+1,m-p)*4^-m,m,p,oo).simplify_full () Here the function c_erf_cheb(p) ends up being -6/11*(bessel_I(6, -9/2) - bessel_I(5, -9/2))*sqrt(e)*e^(-5)/sqrt(pi) which, to me, is a very useful answer. But other sums are simply wrong. k = var('k') sum(x^(2*k)/factorial(2*k),k,0,oo) gives -1/4*sqrt(2)*sqrt(pi)*x^(3/2) but the answer should be sinh(x). For other sums, Sage simply repeats what I told it. sum(x^(3*k)/factorial(2*k),k,0,oo) I understand that Sage has limited exploitation of Maxima's hypergeometric functionality, and I suspect this is the main issue. Are there any conceivable workarounds? -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at http://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.