# Questions tagged [special-functions]

Questions on the special mathematical functions implemented in Mathematica.

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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. ...
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### 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 ...
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: ...
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 ...
30 views

### Jacobian elliptic function argument [closed]

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

### Strange result of LaplaceTransform

I mean LaplaceTransform[BesselI[3, x], x, s] // Simplify ...
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 ...
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### 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 $\theta_3 (q)=1+2\sum_{n\ge 1}q^{n^2}$, $q=e^{\pi i\tau}$, $q^{\lambda}=e^{\pi i\tau \lambda}$, $q\in\mathbb{C}$, $|q|\lt 1$, $\tau\in\mathbb{C}$, ...
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### HurwitzLerchPhi

I am not sure why this is returned unevaluated: HurwitzLerchPhi[1, 1, ∞] Everything is returned unevaluated ...
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 ...
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### 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 ...
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### 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 ...
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=...
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. ...
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 ...
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[...
133 views

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

I have these expressions: ...
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### 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(\...
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. ...
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### 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 ...
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 ...
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: <...