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*I
Probably other parts of Sage as well.
sage: import mpmath
sage: mpmath.hyp2f1?
sage: maxima_console()
(%i1) ? hypergeometric
Asked: 2013-01-07 13:38:25 +0100
Seen: 1,117 times
Last updated: Jan 07 '13
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Are you looking for symbolic manipulations or just numerical evaluations?