# Questions tagged [special-functions]

Questions on the special mathematical functions implemented in Mathematica.

1,130 questions
Filter by
Sorted by
Tagged with
1answer
70 views

2answers
217 views

### Integrating an exponential with upper incomplete gamma functions

I would greatly appreciate calculating an integral consisting of an upper incomplete gamma function and an exponential function. ...
3answers
304 views

1answer
41 views

### Problem when applying FindRoot to a very complicated function [closed]

The error I get when evaluating my code is: FindRoot: The function value [...] is not a list of numbers with dimensions {1} at {q}={2.25}. I have read a lot of questions regarding this error, though ...
0answers
67 views

### How to change Machine Precision digits to meet the tolerances

I am trying to solve for Tcm and Mag by solving nonlinear equations using FindRoot command using following code: ...
3answers
524 views

### Calculating $\lim_{x\to 1} \, \int -\frac{i \text{Li}_2\left(x-x^2\right)}{\sqrt{3} \left(x-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)} \, dx$

How can we force Mathematica to compute this limit? $$\lim_{x\to 1} \, \int -\frac{i \text{Li}_2\left(x-x^2\right)}{\sqrt{3} \left(x-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)} \, dx$$ It seems it ...
0answers
30 views

### Jacobian elliptic function argument [closed]

I have a C++ code that computes jacobian elliptic sn, cn and ...
0answers
38 views

### How can I plot complex functions which take small values?

I would like to know, how can I plot some functions that have oscillating behavior each function can be plot independent. The goal is to show both oscillations even is they are very small values. ...
0answers
54 views

### Strange result of LaplaceTransform

I mean LaplaceTransform[BesselI[3, x], x, s] // Simplify ...
1answer
102 views

### Solve using PolyGamma function

I am trying to solve for the value of y. My code is: x = 0.165; f = -Log[y] - PolyGamma[0.5 + 0.2*(x/y)] + PolyGamma[0.5]; Solve[f == 0, y] Running gave me ...
0answers
61 views

1answer
80 views

### Force EllipticTheta to “use” $(e^{\pi i\tau})^{\lambda}=e^{\pi i\tau \lambda}$

Define $\theta_2 (q)=2\sum_{n\ge 0}q^{(n+1/2)^2}$ and $\theta_3 (q)=1+2\sum_{n\ge 1}q^{n^2}$, $q=e^{\pi i\tau}$, $q^{\lambda}=e^{\pi i\tau \lambda}$, $q\in\mathbb{C}$, $|q|\lt 1$, $\tau\in\mathbb{C}$, ...
1answer
68 views

### HurwitzLerchPhi

I am not sure why this is returned unevaluated: HurwitzLerchPhi[1, 1, ∞] Everything is returned unevaluated ...
1answer
145 views

### Integrate real function returns complex function [closed]

I want to compute the integral $$\int_0^c \exp(-cx+x^2) \mathrm{d}x,$$ where $c>0$ is an unknown constant. In Mathematica Version 12.2.0 ...
1answer
95 views

3answers
134 views

### How to approximate the harmonic sum $\sum_{n=1}^\infty\frac{{4n\choose 2n}\overline{H}_{2n}}{n 2^{4n}} ?$

How to approximate $$\sum_{n=1}^\infty\frac{{4n\choose 2n}\overline{H}_{2n}}{n 2^{4n}} ?$$ Where $\overline{H}_n=\sum_{k=1}^n \frac{(-1)^{k-1}}{k}$ is the skew harmonic number. The mathematica ...
1answer
52 views

### How to define distributivity of CenterDot on bras and kets

I am working on a code for a coupled quantum harmonic oscillator and found myself in a hiccup when trying to evaluate the inner product of linear combinations of bras and kets. I have initially ...
1answer
106 views

### Solve Equation trinomial Nine degree!

I am trying to solve equation: x^9+p*x^4−q==0, {p, q} ∈C using functional analysis. Ηow do I solve this equation and with help Mathematica program for case p=π, q=...
1answer
45 views

### How to find the exponent of Bessel function related infinite integral? [closed]

Please suggest how to find the power law exponent for curvature vs r, I am trying using exponet but it is not working. ...
1answer
297 views

### Find RSolve solution reflecting special structure of DifferenceRoot[Function[{\[FormalY], \[FormalN]}

RSolve yields a large (multi-page) solution (LeafCount=25891) containing a number of 7F6 (and higher) hypergeometric functions when applied to ...
2answers
39 views

### Warning when confluent hypergeometric function HypergeometricU is wrong?

From the definition as an integral (HypergeometricU/details), this function must be positive. However, it gives negative numbers in some cases with no warning of a potential error. For example, In[...
3answers
133 views

### Why does ParametricPlot does not reach the values I expect?

I have these expressions: ...
1answer
90 views

### Legendre's relation for Elliptic Functions not satisfied in Mathematica?

I've been playing around with elliptic integrals lately and I came across Legendre's relation, relating the complete integrals of the first and second kind, $K(k)$ and $E(k)$ respectively: \$E(k)K(\...
0answers
48 views

### Angular functions defined using Wigner D-functions [closed]

How do I properly implement angular functions using Wigner D-functions in Mathematica? Angular functions are commonly used in light scattering calculations and can be defined using Wigner D-functions. ...
0answers
30 views

### How to nicely expand a Gauss Hypergeometric function?

Does anybody know how to obtain the z->1 expansion for the Gauss Hypergeometric 2F1(a,b;c;z) on Mathematica as shown here ? I tried to use Series with the assumption c-a-b non-integer, but the ...
2answers
58 views

### Error in Integration of special functions using mathematica 12.0

When I try to integrate the following, Integrate[-GegenbauerC[22,-1/2,x]/(1+k*x),{x,-1,1}] where -1<k<1 and k!=0, Mathematica gives different results if I ...
2answers
281 views

### Code that produces plot in V5 doesn't work in later versions

I have problem in plotting Integral function. I can compute/plot the graph of this integration below in Mathematica 5.0, but it is not possible to plot it in higher Mathematica versions. My code is: <...
1answer
4k views

### Creating a Mathieu stability diagram

I am attempting to re-create a Mathieu stability diagram like the one shown in a paper by Leary and Schmidt : I expected that I could use MathieuC to generate ...
1answer
46 views

### How to make FindRoot work with PolyLog functions

I have the following code: ...