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How to increase maxterms for hypergeometric?

asked 2019-04-24 09:19:34 -0500

anonymous user

Anonymous

updated 2019-05-06 09:51:17 -0500

Iguananaut gravatar image

I'm trying to compute a (bunch of) hypergeometric functions for which I get a NoConvergence error

e.g.

hypergeometric([4.14 + 15*I, -3.14 + 15*I],[1. - 1.12e7*I], -500000)

The suggestion of the error message is to try increasing 'maxterms'. However, I don't seem to find a way to do this as e.g.hypergeometric([4.14 + 15*I, -3.14 + 15*I],[1. - 1.12e7*I], -500000,maxterms=10^6) does not work.

(I could be missing something very basic, I'm rather new to sage)

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Iguananaut gravatar imageIguananaut ( 2019-04-24 09:37:50 -0500 )edit

Indeed, that is not a very helpful message. It seems that the underlying low-level sage.libs.mpmath.ext_impl.MPF_hypsum function does accept a maxterms argument, but there is a disconnect that prevents this from being passed to it from the higher-level generic hypergeometric function. I would consider this a bug.

Iguananaut gravatar imageIguananaut ( 2019-04-24 09:44:18 -0500 )edit

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answered 2019-04-24 09:59:05 -0500

Iguananaut gravatar image

By digging into the code and going a little lower-level I was able to do effectively the same thing while close-enough to the lower-level code that it accepted the maxterms argument (of course, you shouldn't have to do this at all and I would consider it a bug):

sage: from mpmath import hyper
sage: from sage.libs.mpmath import utils as mpmath_utils
sage: mpmath_utils.call(hyper, [4.14 + 15*I, -3.14 + 15*I],[1. - 1.12e7*I], -500000, maxterms=10^6)
-608213.273405350 - 24201.2928264098*I

I make no guarantee as to the accuracy of the result or if it's even expected be convergent for the given $a$'s and $b$'s.

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Thanks! This indeed works and I will heed your word of caution but mathematica seems to agree ...

virtual_neutrino gravatar imagevirtual_neutrino ( 2019-04-25 06:32:43 -0500 )edit

Great. I went ahead and opened a ticket for the maxtermsissue: https://trac.sagemath.org/ticket/27785 Coincidentally, a different bug involving arguments to hypergeometric was just fixed, but I don't think it has anything to do with this one.

Iguananaut gravatar imageIguananaut ( 2019-05-06 09:51:06 -0500 )edit

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Asked: 2019-04-24 09:19:34 -0500

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Last updated: Apr 24