# Questions tagged [special-functions]

Questions on the special mathematical functions implemented in Mathematica.

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### Using Assumptions in Expressions that Evaluate to be Elliptic Integrals

I have the following integral that I am trying to evaluate in Mathematica: $\int \sqrt{\alpha + m g l \cos(q)} dq$. If $\alpha > m g l$, then the result is a complete elliptic integral of the ...
42 views

### How to find expansion coefficients in Fourier-Legendre

I am trying to find the coefficients for the Fourier-Legendre expansion of a potential. My goal was to obtain the coefficients as expressions in terms of x and y. I followed the example given on the ...
374 views

### The numerics of FresnelS[]

Bug introduced in 12.1 or earlier and persisting through 12.1.1 or later [CASE:4615361] Note: A worse problem existed in 12.0 for inputs greater than 8 and of ...
52 views

### NIntegrate with highly oscilatory result

I want to evaluate a function defined by the following numerical integral: ...
37 views

### Comparing two equivalent definite integrals

Reading this question on Math.SE, I tried the following Mathematica instructions ...
277 views

### Find RSolve solution reflecting special structure of DifferenceRoot[Function[{\[FormalY], \[FormalN]}

RSolve yields a large (multi-page) solution (LeafCount=25891) containing a number of 7F6 (and higher) hypergeometric functions when applied to ...
47 views

### Indefinite Integral not Solving

I'm tring to solve the Indefinite Integral of the function: ...
31 views

### Taking the limit of the derivatives of the Beta function [closed]

I tried using Limit[D[Beta[a,b],{a,1},{b,1}],{a -> 1},{b -> 1}] and Limit[D[Beta[a,b],{a,1},{b,1}],{a , 1},{b , 1}] but it ...
238 views

### Plot of The RiemannSiegelZ Function

I would appreciate your help to visualize the of the following function RiemannSiegelZ[x] with this range. { 18154980120849865 , 18154980120849885 } I tried this: ...
67 views

### Strange behaviour with EllipticTheta functions

For some time I have been using EllipticTheta[3,-,-] functions, and to me it seems that Mathematica is really not handling them in the best way. Below are two of ...
### QPochhammer function simplification?
Consider the function $$(a;q)_n=\begin{cases} 1&n=0,\\ (1-a)(1-aq)\cdots(1-aq^{n-1})&n=1,2,\dots,\\ [(1-aq^{-1})(1-aq^{-2})\cdots(1-aq^n)]^{-1}&n=-1,-2,\dots \end{cases}$$ which in ...