# Tagged Questions

Questions on the special mathematical functions implemented in Mathematica.

93 views

...
100 views

### Spurious infinite limit of integration message in NIntegrate

Bug introduced in 7.0 and persisting through 10.2 NIntegrate returns an error complaining that ComplexInfinity is an invalid ...
289 views

83 views

### speed up evaluating a listable function [duplicate]

I apologize in advance for the vagueness, but I can't think of a more descriptive title. I am trying to find the average value of the square of BesselJ[0, x] ...
609 views

### How to plot Ramanujan's continued fraction in Mathematica?

I want to plot Ramanujan's continued fraction: $$R(q)=\cfrac{q^{1/5}}{1+\cfrac{q}{1+\cfrac{q^2}{1+\ddots}}}$$ but I do not know how to define this function in Mathematica. How do I define and plot ...
190 views

### How can I find all solutions of a complicated expression in a desired interval with Mathematica?

I have an expression which is a combination of Bessel functions: ...
94 views

### PolyLog does not simplify

How come mathematica can not simplify a simple expression involving the PolyLog function? An example is: You know that ...
317 views

### Asymptotics of $\frac{\sum _{i=0}^{\lfloor n/2 \rfloor} {2(n-2i) \choose n-2i} {n \choose 2i} {4i \choose 2i}}{2^{3n - 1}}$

I am fairly sure that asymptotically $$\frac{\sum _{i=0}^{\lfloor n/2 \rfloor} {2(n-2i) \choose n-2i} {n \choose 2i} {4i \choose 2i}}{2^{3n - 1}} \sim \frac{2}{\pi n}.$$ I tried ...
117 views

### Bessel functions and ListContourPlot [closed]

I'm trying to plot some eigenfunctions (for a semicircle) in Mathematica. Functions are of the following form: $$g_{ms}=J_{2m+1}(y_{ms}x) \sin ((2m+1)\varphi)$$ For example, for $m=0$ and $s=1$ it ...
18 views

137 views

...
71 views

### Problem with Erf near Infinity in NSolve

I have to solve a differential equation involving the error function Erf, but my code is not able to evaluate it in the range I need. I think I can formulate my ...
108 views

### Work around bugs in Summation, Hypergeometric function?

I'm so confused I don't even know how to phrase the question, so here's what's happening: I need an analytic form for this: ...
107 views

### Orthogonal Collocation Using Jacobi Polynomials

I'm trying to solve a PDE(diffusion-reaction in a spherical catalyst pellet) using Jacobi Orthogonal Collocation method. But at the stage of solving the system of ODEs(using ...
231 views

### Is MathieuC for moderately large imaginary arguments broken?

I'm trying to plot MathieuC[-3,0.3,I x] for $x\in[0,10]$, and here's what I get even with arbitrary precision arithmetic (here I use ...
74 views

### 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 ...
93 views

### Having trouble interpreting the results DSolve gives for the Laguerre equation

I am trying to solve a second order ODE using Mathematica. Before I get into solving my (more complicated) problem, I am trying to use DSolve on known ODEs to check that the answer that Mathematica ...
87 views

### Why minimization does not work with symbolic array as arguments

If I try to minimize with constraints a function of several variables, with Gamma regularized function involved in the constraints it seems to works, as shown below (this is just a dummy example ...
126 views

### How to define $\operatorname{Mc}$ and $\operatorname{Ms}$ Mathieu functions in terms of MathieuC and MathieuS?

Reading multiple books about Mathieu functions, I always come across notation like $\operatorname{ce}_r(z,q)$, $\operatorname{se}_r(z,q)$ for angular functions and $\operatorname{Ce}_r(z,q)$, ...
133 views

### Imaginary terms in the derivative of Jacobi theta function (2) on the real line

I am trying to calculate/plot the derivative of the second Jacobi theta function $d\theta_2(0, e^{-\pi t} )/dt$. Calculating or plotting the function itself works fine: ...
106 views

### Why is the Spherical Bessel Function acting strangely at this point?

I'm doing some computation that requires the use of Spherical Bessel Functions of the 1st kind, at high orders and values. So, I managed to find this, while running it over a wide range of values. I ...
108 views

### Computational Complexity of HypergeometricPFQ

What is the computational complexity of HypergeometricPFQ? I got a result of a product of a multinomial and HypergeometricPFQ and I was wondering if that would be considered a closed form solution ...
112 views

### Sum over Binomials and Gammas

Given the function, ...
589 views

### Expansion of a hypergeometric function takes ages with Mathematica 9 and 10 (regression?)

Mathematica 8 (Linux version) can evaluate AbsoluteTiming[Series[Hypergeometric2F1[1, 1 - eps/2, 3 - eps, 1/2], {eps, 0, 0}]] in no time. On one of the ...
321 views

### 3D Gamma function

I try to plot the following function: Plot3D[Gamma[1+0.5*(n+m)]/Sqrt[Gamma[1+n]*Gamma[1+m]],{n,0,1000},{m,0,1000}] I expect that for m=n and near to it the value ...
88 views

### Complete definition of special functions in Mathematica [closed]

How can one display the actual integral involved in special functions like this MarcumQ[2, a, b] in Mathematica?
331 views

### Perturbation theory with Mathematica: Definite integral of polynomial times exponential times hypergeometric function of imaginary argument

I would like to ask also Mathematica users about my question from the math forum. To expand, I'm adding the code which calculates the full double integral for $n=0$ and $\mu=0$ (the second in the ...
140 views

### What are the terms of the sequence generated by Zeta(3s)/Zeta(s)?

The LiouvilleLambda function has Dirichlet generating function of Zeta[2s]/Zeta[s]. I am curious about an analogous function with Dirichlet generating function of Zeta[3s]/Zeta[s]. Can Mathematica ...