Tagged Questions

Questions on the special mathematical functions implemented in Mathematica.

0answers
65 views

Why is PolyLog[] giving weird answers for ordinary values? [duplicate]

Possibly related to this question, but it seems slightly different: Strange behaviour of PolyLog Function Wikipedia says that for real s, z<1 should be real. So I was confused when MMa returned: ...
1answer
108 views

Strange timings of integrals involving Hermite's polynomials

I have used Mathematica to calculate tunneling for quantum harmonic oscillator. The code is simple: ...
2answers
109 views

Integrating a compound expression

I have an integral of the form I[r]=∫(arExp[-r]-brSin[k(r-d)]Exp[-r])BesselJ[0,kr]dr where Besse1J[0,kr] is the modified ...
2answers
251 views

Number of divisors visualized with the QPochhammer function, how to improve performance of code?

I have this code that is originally Jeffrey Stopple's code for the Riemann zeta function in the complex plane. Because I discovered yesterday that the number of divisors can be generated with the $q$-...
2answers
115 views

Using Fold to show stages of Euler product formula

I would like to recursively replicate each stage of the Euler product proof. This does it: ...
1answer
115 views

Is there a LogBeta function like the LogGamma?

In a computation, I need Log[Beta[alpha+j,beta-j+n]] of some kind. Is there a LogBeta function built-in to avoid any under/over ...
1answer
238 views

Get rid of Error Function: How to get rid of sequential appearances of error function?

We have a function as e[t_] :=(E^(-t^2)) Cos[0.1 t] and we must evaluate below integration (However I used the variable x ...
2answers
146 views

Inverse of LogIntegral

I wanted the inverse logarithmic intgral, so I typed InverseFunction[LogIntegral] and received the expected symbolic answer. But when I try to integrate it or ...
2answers
371 views

Lower branch of Lambert W function in mathematica

I am interested in values of the Lambert W function, which is defined as the solution to the equation $z = W(z) e^{W(z)} .$ The solution is not, however, single-valued, but branches into two ...
0answers
99 views

Spherical Hankel and Bessel in Explicit form

This is probably an easy question, when I type the spherical Hankel (first kind) and the Bessel function into Wolfram Alpha, it gives back an explicit form, the one you would get if you were to do it ...
0answers
111 views

1answer
178 views

Symbolic integration of elliptic functions

Is there a clever way to integrate products of elliptic functions like $\wp(z;g_2,g_3)$ or $\zeta(z;g_2,g_3)$ in Mathematica? Mathematica seems to be able to integrate functions like ...
1answer
358 views

Expanding derivatives of hypergeometric functions

Sometimes Mathematica expresses results of integration or summation in terms of symbolic derivatives of Hypergeometric2F1 function, and cannot further simplify ...
1answer
131 views

Finding a root of a parameterized integral

I have a function given as a parameterized definite integral: f[a_] := Integrate[BesselJ[0, x - a] BesselJ[0, x + a], {x, -∞, ∞}] I suspect it has a root near <...
1answer
123 views

Numerical evaluation of ChebyshevT

When I evaluate the following Chebyshev series of the first kind in two different ways, I get two very different results: ...
2answers
224 views

Define PolyLog so that positive reals evaluate on upper edge of branch cut

Generalizing the previous question: Define Log so that negative reals evaluate on lower edge of branch For real positive values $x>1$, Mathematica's polylogarithm function ...
1answer
252 views

How to calculate the unknown quantity in an infinite series?

I'd like to calculate x value in this equation. Basically, I tried to 2 types of method which are FindRoot and NSolve. But, I have failed the calculation caused by these errors up to now. If there ...
1answer
173 views

Cannot solve equation

I just started using mathematica and I'm facing a problem that I just can't solve. I want to solve the following equation: Code: ...
1answer
720 views

HarmonicNumber problem

I am looking for all the roots of HarmonicNumber, in the domain [-30, 1] and [0, 6000] for the real and imaginary parts, respectively, and where the parameter ...
2answers
268 views

A regularized hypergeometric function related question

I'm interested in finding a way (if possible) of expressing this specific value of the regularized hypergeometric function in terms of known constants. How might I use Mathematica to check this ...
1answer
510 views

How to use FindRoot to solve an equation containing a parameter?

I'm trying to derive some of the results of the following paper: Electrodynamics of semiconductor-coated noble metal nanoshells, JT Manassah - Physical Review A In the paper there is matrix \$\mathbf ...
1answer
146 views

What is the formula Mathematica uses for ZetaZero?

What is the formula/algorithm Mathematica uses for the ZetaZero command?
2answers
487 views

Bessel derivatives

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