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hypergeometric function 2F1 with in Sage

asked 2013-01-07 06:38:25 -0500

TKGunter gravatar image

updated 2013-01-07 06:46:57 -0500

DSM gravatar image

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?

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Are you looking for symbolic manipulations or just numerical evaluations?

DSM gravatar imageDSM ( 2013-01-07 06:45:36 -0500 )edit

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answered 2013-01-07 07:17:05 -0500

kcrisman gravatar image

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.

Mpmath:

sage: import mpmath
sage: mpmath.hyp2f1(2,3,4,5)
mpc(real='0.15654212933375475', imag='0.15079644737231007')

Maxima:

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.

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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.

TKGunter gravatar imageTKGunter ( 2013-01-07 08:33:52 -0500 )edit
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answered 2013-01-07 07:11:53 -0500

achrzesz gravatar image
sage: import mpmath 
sage: mpmath.hyp2f1? 

sage: maxima_console() 
(%i1) ? hypergeometric
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Asked: 2013-01-07 06:38:25 -0500

Seen: 519 times

Last updated: Jan 07 '13