# Questions tagged [special-functions]

Questions on the special mathematical functions implemented in Mathematica.

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### is the Fox-Wright Psi solution of the trinomial equation implemented in mathematica?

According to (13.4) in Belkic: the trinomial roots, their powers and logarithms from the Lambert series, Bell polynomials and Fox–Wright function https://d-nb.info/1176090631/34 the solution of ...
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### Problem evaluating numerical value of MeijerG[] function at some parameter?

I need to evaluate this sum: Where x = 33.6614 and $k,l,s$ are non-negative index of the three sum. For example $k,l,s=0,1,2,3,...$. Furthermore, $M$ is a positive integer that is $M=1,2,3,4...$ ...
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### NSolve with Bessel and Hankel functions

I have a complicated function that I would like to solve for the roots. The function comprises Bessel and Hankel functions: ...
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### How to find the equivalence Matlab code for Mathematica Meijer-G function in this case? [closed]

During my calculation, I end up receiving a strange function called the meijerG function with the Mathematica syntax ...
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### Calculating a particular MeijerG function [closed]

I want to calculate this following MeijerG function...I used this command MeijerG[{{1/2 - s, 1 - s}, {-s}}, {{0}, {-s, 1/2}}, Abs[x]^2] but Mathematica can not ...
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### Integral giving a Dirac delta

I have the following type of integral Integrate[ r BesselJ[n, a r] BesselJ[n, b r], {r, 0, Infinity} (where a and ...
376 views

### How to find the sum of that series related to Legendre functions of the second kind?

I mean $$\sum _{n=0}^{\infty } \frac{Q_n\left(\frac{\sqrt{2}}{2}\right)}{n+1}.$$ It's unclear to me whether the series under consideration converges. I have strong doubts concerning its closed form. ...
37 views

### Find the numerical value of the 2nd positive solution of a Bessel Function [closed]

A) Find the numerical value of the 2nd positive solution of $J_2 (3x)=0$ to at least 5 significant digits Note: $J_n(y)$ represents a Bessel function, which is written as ...
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### Why can't Mathematica evaluate this integral?

I want to work with the rectangle function, which I define by f[x_, m_] := Limit[1/((2*(x - m))^(2*k) + 1), k -> Infinity]; (I know that in theory I can use <...
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### Integration of product of BesselJ and BesselY not giving correct results

I am trying to integrate a product of Bessel functions as shown below. Where z is real valued and positive. The integration yields MeijerG functions. Taking a ratio of the derivative of the MeijerG ...
44 views

### How to programmatically Evaluate Notebook (all cells in an open notebook) rather than from Evaluation menu? [duplicate]

I am working on a DockedCells toolbar for common tasks like Save, ClearAll, scrolling, etc., ...
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### expansion of hypergeometric series [closed]

I am completely new to mathematica. I am not sure how to calculate the expression 2F1. Is it possible to a closed form solution in terms of z of the hypergeometric series 2F1(-a, N/2-a, N/2; z) and ...
32 views

### Adding a module to teach Mathematica the Laplace transform of particular Mittag-Leffler functions

Mathematica 11.3 is not aware of a useful Laplace transform LaplaceTransform[t^(-a) MittagLefflerE[a, a, t^a], t, s] which for ...
44 views

### Plotting a Legendre Polynomial

currently I am trying to plot for the Legendre polynomial $P_n(x)$ for $n=0,1,2,3,4$ and $-1 \leq x \leq 1$ . To plot for it, I wrote the following code: ...
102 views

### Why does Integrate get this wrong?

Why does Integrate get this wrong? ...
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### Exact value involving ProductLog

By manual manipulation, it's not too difficult to show that the value of the following expression is exactly $1.$ How to convince Mathematica to do the simplification? ...
71 views

### Precompute Functions for use in NDSolve [closed]

I have a very complicated pair of functions $F(x,y), G(x,y)$ that are used in a differential equation $0 = x'' + F(x,y)$, $0 =y '' + G(x,y)\,.$ $F$ and $G$ are roughly sums of products of the Bessel ...
71 views

### Error in Creating Orthogonal Polynomials

I'm trying to create my own set of polynomials orthogonal to weight $w(x)=x^{14}$ on $[-a,a]$. My code: ...
69 views

### How to Integrate this expression?

All the parameters ($r, b,$ and $q$) are real and positive. Is it possible to do the below integration? ...
57 views

### How to DSolve this differential equation?

How can I find h[r] from this equation? I need h[r] or its r derivative. ...
42 views

### Non-Convergence In Creating Legendre Series

I'm trying to use Mathematica to create a Legendre-Fourier series using this Wikipedia article. Here is my code: ...