# Questions tagged [special-functions]

Questions on the special mathematical functions implemented in Mathematica.

1,178 questions
Filter by
Sorted by
Tagged with
68 views

### Example in Help File does not evaluate as claimed

In the help file, under BellB, I read at "Properties and Relations": Sum can give results involving ...
999 views

157 views

### Finding Values of All Nine Constants in q-hypergeometric Equation

I suspect that an identity of the form $$\sum_{j=-n}^{j=n}(-1)^jq^{j(5j+1)/2}=\sum_{r=0}^{n}f_{ar+bn+c}(-1)^{n-r}q^{(n-r)(dr+en+f)/2}\frac{(q;q)_{gr+hn+j}}{(q;q)_{n-r}}$$ for $a, \dots , j$ integer ...
560 views

### Computing a sum

I'm trying to make Mathematica compute this sum: Sum[(-1)^k (n - k)^2 Binomial[2 n, k], {k, 0, n}] As is, I get an awful formula: ...
210 views

### What is the formula Mathematica uses for ZetaZero?

What is the formula/algorithm Mathematica uses for the ZetaZero command?
243 views

### Symbolic integral including Hermite polynomial does not evaluate

I am trying to evaluate the following integral: Integrate[HermiteH[n, Sqrt[a]* x] * Exp[- (c/2)* (x^2 + y^2) + b* x * y - (a * x^2)/2], {x, - Infinity, Infinity}] ...
2k views

### Bessel derivatives

I tried to expand BesselJ[k,x] function into a Taylor series with Series command. Here both k...
411 views

### How to choose a solution of a differential equation?

I am trying to solve the following differential equation: ...
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 ...
2k views

### Are solid spherical harmonics implemented in Mathematica?

In certain applications, solid spherical harmonics can be very useful. They are essentially the usual, 'surface' spherical harmonics, with the appropriate power of the radius inserted: S_l^m(x,y,z)=...
589 views

### Evaluating Erf[x] in arbitrary precision

Is it possible to evaluate Erf with arbitrary precision? I only get 1. as result but I would like to know if a arbitrary ...
1k views

### Is there a function for falling factorial in Mathematica

If I had to construct a function for falling factorial in mathematica I'd do something like that (hope I'm not mistaken): fallfact[x_,k_]:=$\prod_{j=0}^{k-1}(x-j)$ But is there a built-in function ...
447 views

### Binomial[-1,-1]

According to various sources e.g. http://www.proofwiki.org/wiki/Definition:Binomial_Coefficient and Wolfram themselves http://functions.wolfram.com/GammaBetaErf/Binomial/02/ , the binomial ...
416 views

### Symbolically Expanding One-Variable $q$-hypergeometric Series

In general, how do I get Mathematica to symbolically expand various infinite series to an arbitrary degree of accuracy? I deal with $q$-hypergeometric series quite frequently, and specifically want ...
188 views

### How can I compute the real part of $\zeta^2$ numerically? [duplicate]

I want to compute and plot $\Re(\zeta(x+iy)^2)$ and $\Im(\zeta(x+iy)^2)$. How can I do that with Mathematica?
225 views

### Symbolic derivatives of special functions yield incorrect results

When I evaluate with Mathematica this expression D[ Abs[ Zeta[x + I y]], {x, 2}] + D[ Abs[ Zeta[x + I y]], {y, 2}] 0 the ...
900 views

### What is wrong in my calculation with Clebsch-Gordan coefficients?

According to theory of angular momentum here, this must equal one. What's wrong? ...
343 views

### Equation involving hypergeometric functions

I want to solve this equation but nor NSolve nor Solve are able to do this. ...
I've never used Mathematica before and am trying to numerically solve equation (12) from this paper. Ideally I'd be able to find the smallest value of $x_{n\nu}$ for $\exp(-kr\pi)$ close to 1, and ...