# Questions tagged [special-functions]

Questions on the special mathematical functions implemented in Mathematica.

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### Simplification of expression with PolyLog[4,2]

I am trying to simplify the following expression. expr=1/2 \[Pi]^2 Log[2]^2-2/3 I \[Pi] Log[2]^3-4 PolyLog[4,2]+7/2 Log[2] Zeta[3] This ...
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1 vote
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### How to compile inverse error function?

I have the following code: ...
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1 vote
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### Strange behavior of error function series expansion at infinity

Evaluating Normal[Series[1/ (1 + xi Erf[xi]), {xi, ∞, 2}]] Normal[Series[1/( xi (1/xi + Erf[xi])), {xi, ∞, 2}]] gives ...
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1 vote
109 views

### Limit of Hypergeometric Functions

Mathematica (12) seems to have a lot of trouble with taking limits involving hypergeometric functions. A simple example I am interested in is the following ...
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1 vote
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### Mathieu Floquet solution

Mathematica provides the MathieuC[a,q,z] and MathieuS[a,q,z] functions - as well as some other Mathieu-related functions. Maple ...
52 views

### Euler angles and WignerD, a question of signs

Express a 3D point as a linear combination of Spherical Harmonics, then rotate that point to a new position and find the new expansion in SH : ...
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1 vote
75 views

### Elliptic theta function wont evaluate [closed]

It appears that Mathematica wont evaluate the Jacobi theta functions when the last argument has a magnitude greater than 1, for example: EllipticTheta[1, 1.5, 0.9] ...
• 151
120 views

### Simplify inverse of function

This would be a noob question, but I need help simplifying the inverse of an expression ...
1 vote
71 views

### Solving a non-algebraic equation at the symbolic level [closed]

Versions 10, 11, 12, 13.0.0.0 and 13.2.0.0 solves the following system of equations ...
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### Time independent perturbation theory for solving coupled differential equations

The eqexact1 and eqexact2 are the coupled differential equation of motion with g lets say a repulsive factor, that I choose. ...
1 vote
82 views

### Series expansion message with special functions

I am trying to expand the following expression in alp,eps. Since the expression involves Hypergeometric2F1, I am using HypExp. <...
• 1,888
1 vote
128 views

### Can the Debye functions be implemented using built-in functions?

It is claimed in the comments here that the Debye functions can be implemented using built-in special functions. This is clearly true for some Debye functions, e.g., $D_n^{(1)}(x)$ for $n = 1, 2, 3$ (...
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### Evaluate the time average of Mathieu functions

I defined a function composed of Mathieu's periodic functions: ...
61 views

### Derivative[0, 1, 1][QPolyGamma] cannot be calculated numerically?

During a more complicated calculation, I got an expression ...
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