# Questions tagged [special-functions]

Questions on the special mathematical functions implemented in Mathematica.

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145 views

### How to express Bessel Functions in terms of Hankel Functions

I have the following expression BesselJ[\[ImaginaryI]*m, k*r] FunctionExpand knows how to transform from ...
51 views

### Calculating complex integral representation of the Hankel function of the first kind

I was wondering if any one can help me calculate this integral using Mathematica. This is a form of integral representation of Hankel function of first kind: ...
130 views

### How do I avoid the singularities during the calculation of an integral?

I face a serious problem when I try to calculate the following integral. My code is the following: ...
44 views

### Error complex function ERFI(X): looking for alternative function representations?

I have some analytical results from a physics problem, where the Mathematica gives the results in terms of complex error function. I would like to explore another function representation using ...
148 views

### How to programmatically change CellStyle of all Cells from "Input" to "Code"?

I have a special notebook styled for only creating functions and their packages. I often lazily do Evaluate Notebook instead of finding and opening all cells I need ...
113 views

### Possible bug in asymptotic expansion of CoshIntegral and SinhIntegral at infinity

Consider this expansion Series[CoshIntegral[z], {z, \[Infinity], 0}, Assumptions -> z > 0]// Normal (* -((I [Pi])/2) + Cosh[z]/z^2 + Sinh[z]/z *) Here a ...
150 views

### Differential Equation in Complex Plane

I asked this question 8 years ago, but the answer of @Jens was not satisfactory and it didn't reproduce the plot exactly. I'm wondering if new versions of Mathematica can handle it.
54 views

### Why does Mathematica only solve this indefinite integral for two values of n?

I'm trying to estimate this integrate: where "a" and "b" are real constants and n> 0. I use the code ...
47 views

### How to use only real values in a notebook?

I am wondering how to make Mathematica only evaluate real numbers by creating an initialization line in the beginning of a notebook. I would like to prevent the following: complex trigonometric ...
433 views

### Why can't Mathematica evaluate the limit of this hypergeometric function? Is there any way to find the answer?

I have the following function ...
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### MeijerG function: numerical evaluation of its derivative

Mathematica does not evaluate the derivative of the following MeijerG function. ...
25 views

### ComplexInfinity only encountered with ColorFunction when plotting HurwitzZeta

I am using Mathematica 11, I am plotting HurwitzZeta[2,x] and its curvature on x$\in$[1,4]. Everything is fine when I try to plot the two. ...
111 views

### Unpacking a Mathematica expression returned by DSolve

I was trying to solve a system of differential equations in Mathematica and had troubles understanding what the solution looked like. So I wanted help to unpack it. I had a system of two coupled ...
82 views

### Issues with an equation involving Logs and PolyLogs

I want to check a claimed identity that involves Log and PolyLog functions. The relation can be found on this paper and more ...
306 views

### How does mathematica numerically evaluate the Meijer G-function?

The Meijer G-function is defined as a contour integral in the complex plane. Mathematica is able to numerically evaluate such a function quickly and accurately. How does she do that?
68 views

### How do I come up with an equation that will describe the results of other integrals with changes to a constant?

I have one equation: 10*(1-x)(x^n)+(x)(1-x^n), to which I must find the integral of from [0,1], with n ranging from 1 to 100. I want to then plot the results with the x value as the value of n and the ...
66 views

### Microfluctuations analysis and Power spectrum

I measured a parameter over time and obtained the values below: 0,627896 0,205004 0,259237 1,059125 0,832184 0,587992 0,565537 0,527323 0,460228 0,471958 0,26696 0,75367 ...
71 views

### Errors when plotting $\operatorname{Re}\sum_{n=1}^{200} \frac{(a\ln x)^n}{n!\, n\zeta (n+1)}$ in $x$

Let $a=1/2-30.424876126i$ ($i^2=-1$). Then trying to plot $$\operatorname{Re}\sum_{n=1}^{200} \frac{(a\ln x)^n}{n!\, n\zeta (n+1)}$$ in $x$ leads to a very inaccurate jaggy graph possibly caused by ...
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### Simplifying hypergeometric function 4F3

I am trying to make Mathematica simplify the following expression below. ...
45 views

### How to create and store a plot for each iteration of a Do loop

I have created the following code below. Its purpose is for me to divide the plot into grids and for each grid I reterive the center point's co-ordinates. ...
41 views

### Converting HyperInt Hlog to Polylogtool G [closed]

how do I replace efficiently HyperInt's Hlog (in maple expression) {Hlog(Y,),Hlog(X, [1, -Y + 1]),Hlog(X,[1,1,1])} in an expression into PolyLogTool G: {G[1,Y],G[1,-Y+1,X],G[1,1,1,X]} Basically, ...