# Questions tagged [special-functions]

Questions on the special mathematical functions implemented in Mathematica.

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### How to write a specific Bessel function in Mathematica

I want to plot the following function on Mathematica, and I gave it a go on wolframalpha. Bessel[n,z] is the usual form, but I am not sure how to use this to compute the following plot: \begin{...
• 235
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### Can Mathematica calculate this elliptic, triple integral?

Integrate[(4 a b/Pi) (a^2 + b^2 - 2 a b Cos[c])^(1/2), {a, 0, 1}, {b, 0, 1}, {c, 0, Pi}] I'm using basic plan, it gives me the result like that. The ...
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1 vote
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### The inverse Laplace transform alters parameter constraints

I have this Laplace transform: $$\left( w \frac{L}{L+s}+(1-w) \frac{Q}{Q+s}\right)^n \ for \ L>0, Q>0,0<w<1.\ (1)$$ ...
• 187
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### Bugs in hypergeometric functions with negative integer lower parameters

If you were to evaluate these expressions, Mathematica returns the value shown. ...
• 61
1 vote
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### How to plot the perimeter of an ellipse where the variable is its eccentricity?

I'm basically just trying to plot a function where the x value is the eccentricity of an ellipse and the y value its perimeter. I've tried first defining the eccentricity ...
• 11
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### A strange behaviour with function $\,_2F_1$

I posted today a question on MSE 1 u=(5*(49*Pi^2*Zeta[3] - 558*Zeta[5]))/(77*Pi^2*Zeta[3] - 930*Zeta[5]) f[k_]:= Hypergeometric2F1[1/2, -k, 3/2, u] Computing <...
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### Computing the elliptic integral $\int \frac{1}{x \sqrt{f+\frac{a}{x^3}-\frac{k}{x^2}}} \, dx$

I don't know how to solve this with or without Rubi?!! ...
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1 vote
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### Hypergeometric function plot [closed]

I can't plot this??!! if you can check this thank you. ...
• 381
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### Simplifying a Sum to GammaRegularized

It doesn't seem Mathematica will automatically simplify Sum[Exp[-x] x^m / m!, {m,0,5}] to GammaRegularized[6,x] Is there a way ...
90 views

### How to calculate the sum of the series of Hermite polynomial?

I want to calculate the infinite sum of Hermite polynomials, which works fine with older versions of Mathematica, but with version 13 it doesn't. The infinite sum is: ...
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### Solving elliptic integrals in Mathematica

I have an integral $$\int_{a2}^{a1}\frac{dx}{\sqrt{(a1 -x)(a2 - x)(a3 - x)}}$$ And I'm trying to integrate it with ...
• 151
1 vote
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### Plotting the Jacobi Elliptic functions

I have a function $$f(x) = a_2 + (a_3 - a_2)\text{cn}^2\left(\frac{\sqrt{a_3 - a_1}}{\sqrt2};m \right)$$ Where $m$ is the modulus, given by $m = (a_3-a_2)/(a_3-a_1)$. How can I plot this function in ...
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### Why does CapForm behave strange with different options? [closed]

This CapForm works well: Graphics[{CapForm["Square"], Thickness[.1], Line[{{-1, -1}, {1, 1}}]}, PlotRange -> 1.5, PlotLabel -> "Square"] ...
• 1,750
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### How to Solve a set of equations

I would like to solve the following two equations. For that I tried Findroot and solve function ...
1 vote
147 views

### Hypergeometric function limit to Cosh[] or Sin[] [closed]

I have this hypergeometric function I woluld like to see in which condition goes to Cosh[] o Sin[] Sqrt[1/a] x Hypergeometric2F1[1/2, 1/b, 1 + 1/b, -(f x^b)/a] ...
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