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Integration from AppellF1[a, b_1, b_2, c, z_1(r,\teta), z_2(r,\teta)]?

Posted 9 years ago

Hello,

I’m working with Mathematica 7.0 and need to integrate from an Appell hypergeometric function F1. My function the integration of which is needed has the following form: AppellF1[½, ½ , ½, 3/2, z1(r,\teta), z2(r,\teta)] and I need to calculate Integrate[AppellF1[½, ½ , ½, 3/2, z1(r,\teta), z_2(r,\teta)],r] While I found the integration formulation of g[z1, z2]:=AppellF1[a, b1, b2, c, z1, z2] in functions.wolfram.com, Mathematica 7.0 is not able to give the response of the integration for g[z1, z2] with respect to z1 or z2.

It may be due to the version of Mathematica which I’m using and it is required to upgrade it?

In general, since z1 and z2 in my function are related to variables (r and \teta) it is possible to calculate such integration with Mathematica? Thank you very much for any responses!

Attachments:
POSTED BY: Maryam Tab
3 Replies
Posted 9 years ago

I observe the same thing you do with respect to the functions page for AppellF1, V10 doesn't give those results when attempting those integrals. And there might be a typo on the page where the subtitle says it is showing integrals with respect to z2, but one of those is showing z1. Perhaps someone can verify that and clean that up if it is incorrect. Thanks.

I also tried your integrals with your constants and V10 cannot seem to find the results for your integrals.

As I mentioned previously, if a numerical integration might be sufficient then this might be possible, but when I tried that it took a very long time and gave warnings about possible singularity or oscillation.

I'm sorry that I can't provide more, but perhaps with your additional information this will coax someone with more skill than I to take a look at your problem.

POSTED BY: Bill Simpson
Posted 9 years ago

Thank you very much for your response, Bill Simpson.

I determined domains of variables, assigned specific numbers to the parameters of denominator, and ignored Sign[], but I’m not able to obtain its integration (as it has been attached).

In addition, I cannot understand while wolfram has presented indefinite integration for AppellF1

It is not possible for me to solve their mentioned integration and obtain their mentioned result using Mathematica 7.0. Am I missing something? Thank you!

Attachments:
POSTED BY: Maryam Tab
Posted 9 years ago

The Sign[] in the denominator is perhaps making it much more difficult to integrate, but even removing the Sign[] does not help.

Not knowing anything about the domain of the variables and whether the denominator might be zero is perhaps making it more difficult to integrate.

Can you provide any additional information as Assumptions to help Integrate?

Version 10 does not appear to be any better able to integrate this without any assumptions.

If you could provide ranges for all variables then you might be able to get an approximate definite integral if that would help you.

POSTED BY: Bill Simpson
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