Hello all I've recently began using sage as an alternative to Mathematica, how ever I have not found the sage equivalent to the hypergeometric 2F1 equation. I have looked through the documentation and have found the hypergeometric_U which is used for the 1F1 equation yet this equation is not useful to me. Is there a 2F1 function already implemented within Sage?
See Trac 2516 for the present status of "symbolic" hypergeometric functions. However, as DSM is alluding, we have a number of ways to get them.
sage: import mpmath
sage: mpmath.hyp2f1(2,3,4,5)
mpc(real='0.15654212933375475', imag='0.15079644737231007')sage: maxima.hgfred([2,3],[4],5)
3*(8*(log(-4)/25-1/20)+16*(13/400-2*log(-4)/125))/4
sage: maxima.hgfred([2,3],[4],5).n()
0.156542129333755 + 0.150796447372310*IProbably other parts of Sage as well.
I'm using the hypergeometric function for numerical analysis, but it's good to know the status of the symbolic manipulations as well. Any who the answers worked like a charm. Thanks all.
sage: import mpmath
sage: mpmath.hyp2f1?
sage: maxima_console()
(%i1) ? hypergeometricAsked: 12 years ago
Seen: 1,160 times
Last updated: Jan 07 '13
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Are you looking for symbolic manipulations or just numerical evaluations?