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## Complex arguments in Hypergeometric Functions

Hello,

After reviewing the documentation for hypergeometric functions, Mathcad Prime 3.0 does not accept comlex numbers as arguments for this type of functions.

I am wondering if anyone has found a workaround this hurdle or is it just simply not possible at all in Mathcad to compute results of hypergeometric functions with complex arguments.

Maybe it's time to move on to a more capable software?

Regards,

Josué

5 REPLIES 5

## Re: Complex arguments in Hypergeometric Functions

Does the Prime symbolic processor have hypergeom and, if so, will it compute floating poing complex results?

Stuart

(The M14 hypergeom float example doesn't work on my installation for some reason - it just simplifies the arguments but doesn't calculate the function).

## Re: Complex arguments in Hypergeometric Functions

 Josue Adorno Nunez wrote:Hello,After reviewing the documentation for hypergeometric functions, Mathcad Prime 3.0 does not accept comlex numbers as arguments for this type of functions.I am wondering if anyone has found a workaround this hurdle or is it just simply not possible at all in Mathcad to compute results of hypergeometric functions with complex arguments.Maybe it's time to move on to a more capable software?Thanks in advance for your help.Regards,Josué

It's possible to write complex versions of the hypergeometric function. The ease of doing so, and accuracy, depends upon which variants you want and the domain of the input arguments (eg, for a general F(a,b,z) with complex vector a and b, you might want only want 1F1 (confluent) or 2F1 (gauss) over some limited set of a and b values).

Stuart

## Re: Complex arguments in Hypergeometric Functions

HI Stuart et al.

My situation is the following: I'm solving the heat equation for a triangular fin in transient state. Using separation of variables I get to a Sturm Liouville equation, which I'm transforming into the Kummer equation. The argument becomes 2λxi. Mathcad will not allow me to use such an argument for the mhyper function. FYI, both λ and x and real numbers and mhyper is either 1F1(a, b, x) or M(a, b, x), per Mathcad Help file. However, I do not know how could I choose either one. Moreover the values of a and b are fixed by the particulars of the problem.

As always, your comments are appreciated and welcomed.

Thanks again,

Josué

## Re: Complex arguments in Hypergeometric Functions

 Josue Adorno Nunez wrote:My situation is the following: I'm solving the heat equation for a triangular fin in transient state. Using separation of variables I get to a Sturm Liouville equation, which I'm transforming into the Kummer equation. The argument becomes 2λxi. Mathcad will not allow me to use such an argument for the mhyper function. FYI, both λ and x and real numbers and mhyper is either 1F1(a, b, x) or M(a, b, x), per Mathcad Help file. However, I do not know how could I choose either one. Moreover the values of a and b are fixed by the particulars of the problem.

Unfortunately, I'm Mathcadless for a couple of days so can't test out an implementation or check what distinction the Help may make. However, I think 1F1 and M are identities. I've got a complex implementation of M on one of my worksheets ... I was playing around with Pearson's Master's thesis and converted a couple of the functions from Matlab to Mathcad - see http://math.stackexchange.com/questions/478052/fast-matlab-code-for-hypergeometric-function-2f-1

Stuart