Problem with the symbolic hypergeometric function

[Fred_Kohlhepp]

I was trying to simplify a calculation, and the symbolic processor returned a response with this function. The symbollic answer lists four arguments then will not evaluate or even recognize the function. (See attached.)

Other references have four arguments, the MatLab web page says MuPad lists 3.

Anyone have a numerical evaluation?

[RichardJ]

It should have three arguments, so that's a bug. Given that, I don't know what to make of the symbolic result, or how to convert it to anything useful. I tried this using the old Maple engine, but that does not give any solution.

[Fred_Kohlhepp]

That's what I was afraid of; this problem is nothin' but trouble.

[StuartBruff]

I'm not sure it's a bug, so much as a Very Undocumented Feature. It looked to me as if it might represent one of the hypergeometric function special cases (eg ₂F₁. Looking at the Quicksheet shows that the builtin fhyper(a, b, c, x) function is the same as hypergeom(n,d,x) for n = (a b) and d = (c). Indeed ₂F₁ is the same thing as fhyper and ₂F₁(a, b; c; x) is a fairly common notation.

If you look at the Mathworks Mupad help for hypergeometric, you can see this notation in one of the examples.

hypergeom([-3, a], [b], z) =

Simplify(hypergeom([-3, a], [b], z))

Typing fhyper(ex+1, 1-a, ex+2, 1-t) gives the answer 0.92. Putting values for b and c of 0. and 0.5, respectively, gives a value for the integral of 0.39.

I also plugged the expression into Wolfram Alpha and it returned the following integral (note that I changed ex to z as ex somewhat confused the interpreter):

Putting this into Mathcad gives 0.253 ...

Stuart

[StuartBruff · Accepted solution]

Oh ... forgot to add a check ...

I've just tried the integral in MuPad (Matlab 2014b variant) and it can't find the integral.

Stuart

[Fred_Kohlhepp]

Thanks much.