# Tagged Questions

Questions on the special mathematical functions implemented in Mathematica.

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### Precompiling a Whittaker function

Is there a way to speed up the evaluation of special functions in Mathematica? I am particularly interested in the Whittaker W function. For instance, the following piece of code: ...
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### Calculating the numerical value of the regularized generalized hypergeometric function

I'm trying to calculate the numerical value of the regularized generalized hypergeometric functions: $\qquad \sf{HypergeometricPFQRegularized}^{(\{1\},\{0,0\},0)}(\{-1.5\},\{-1.,-0.5\},3600.)$ I ...
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### Integration result with incomplete beta function

I'm doing some calculations (double integration) which results in the incomplete beta function occurring as an end result. My input is: ...
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### Solution to Simultaneous Arithmetic/Geometric Mean Recursion Relations

I'm trying to solve the simultaneous convergent sequences of geometric/arithmetic means where $a_{n+1}=\frac{1}{2}(a_n+b_n)$ and $b_{n+1}=\sqrt{a_nb_n}$ and initial values are $a_0=1+x$ and $b_0=1-x$. ...
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### Can anyone re-produce this result related to the spectrum of Riemann Zeta using error term generated from MangoldtLambda?

All: I tried to reproduce the results from this page: How to plot the Riemann-Zeta zero spectrum The following is the code that was posted on above page: ...
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### Plotting precise intersections involving singular functions

I have pseudo-elliptic functions defined on a parallelogram within $\mathbb{C}$ and I would like to clearly highlight the path within this parallelogram which satisfies the real part of my pseudo-...
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### Determine class of special function from algebraic constraints?

Consider vectors x_i in arbitrary dimension. Let's say I have an expression in six variables F[x_1,x_2,x_3][x_4,x_5,x_6], which ...
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### Why can't I use OmegaPrime to find the Limit of Prime[n]? [duplicate]

I've looked at these links already; What are the limits of the Prime-functions? What is so special about Prime? which gave an answer for earlier versions of Mathematica. Yet when I try to input ...
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### How to plot zeros of confluent hypergeometric function

I am fairly new to mathematica so I need a little bit of help. I need to plot the zeros of an equation containing confluent hypergeometric functions. The equation i need to solve is given by the ...
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### Solve an equation that include Gamma

I want to solve the following equation Solve[Gamma[1 + x]/Gamma[x - 1/2] + 1 == 0, x] I have answer x=-0.25, but I can not obtain this answer with Mathematica. ...
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### Use Solve[] with Bessel, gamma, and hypergeometric functions?

I need to find values of {a,b,c} such that the 0th, 2nd, and 4th order moments of f[x]=Exp[-ax^4 - bx^2 - c] will equal respectively {1,2,10}. I didn't really expect this to work, and it didn't: <...
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### Storing Variables in “Loops” and Point Plotting

Given the function $y=\sin x$ defined over the region $-\pi \leq x \leq \pi$, I need to implement a "do loop" such that I sweep over 100 or so points $-1 \leq y \leq 1$ and find precisely the two $x$ ...
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### Inverse of a Digamma/ Polygamma Function

How one can find the inverse of a digamma/ Polygamma function in Mathematica 10?
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### Simplify expression to Integer

I have the following function: f[n_]:=(n-1) E Gamma[n,1]; I know that this expression always evaluates to an Integer, but Mathematica doesn't always output the ...
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### Unexpected Weierstrass $\wp$-Function Behavior

In Mathematica, the Weierstrass $\wp$-function is expressed by WeierstrassP[u + I v, {g₂, g₃}] where g₂ and ...
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### Why is the indefinite integral $e^\frac{x}{2}x^\frac{g}{2}dx$ the upper Gamma function in Mathematica? [closed]

I have an indefinite integral $e^\frac{x}{2}x^\frac{g}{2}dx$, I try to solve in Mathematica. Solve[Int[e^{x/2}x^{g/2-1}dx ,x]] (* Gamma[g/2,x/2] *) How does ...
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### ParametricPlot with 2 variables

I want to try plotting this: As you can see the first axis is v and the second is just dependent of the angle of $\Phi$ . The function is ...
### How I can integrate $\int_0^{a} x e^{-\frac{b^2 x^2}{2 c}} J_0(n x) dx$?
How can I get a solution to the integral given below ? $\quad \quad \int_0^{a} x e^{-\frac{b^2 x^2}{2 c}} J_0(n x) dx$ where $a,\,b,\,c$ and $n$ are constants and $J_0$ is a Bessel function of the ...