Questions on the special mathematical functions implemented in Mathematica.

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4
votes
2answers
253 views

Numerical Integration with InverseErfc

I am trying to numerically integrate an equation that involves InverseErfc (embedded in the copula defined). The equation looks like the following: $$ \int_0^T \int_0^\infty \int_0^\infty ...
0
votes
1answer
336 views

Searching for roots of complex function

I'm searching for roots of complex function $$ 2\imath q \ln(-2\imath k)+\imath\pi-2\imath \Im(\ln(\Gamma(1+2\imath q)))+\ln(\frac{\Gamma(1+\imath q-\imath q x/k)}{\Gamma(1-\imath q-\imath q ...
15
votes
0answers
591 views

Fast Spherical Harmonics radiative transfer

This is a rather specific question and I apologize for spamming you with some lengthy code. But it could be interesting for some reader and maybe you can help out, so please bear with me. I am using ...
7
votes
0answers
509 views

Inverse Laplace transform not obtained

I can't seem to be able to compute the inverse Laplace transform of a Laplace transform: ...
6
votes
0answers
134 views

Using FunctionExpand to evaluate symbolic derivatives

Some symbolic derivatives of certain special function are not expanded automatically, but FunctionExpand often helps to get a derivative-free closed form ...
6
votes
0answers
290 views

Reproducing the Integral Definition of the Modified Bessel function

I need to simplify some integral expressions in terms of special functions, such as the modified Bessel function of the first kind. See for example Eq. (5) on this page. Notice that the real ...
5
votes
0answers
99 views

Expansion of $E(i c \mid m)$ at $c\to\infty$?

Currently, I am using a Windows machine with Mathematica 8. I noticed a difference in a series expansion of the function EllipticE[] in comparison with a result ...
3
votes
0answers
52 views

SiegelTheta fails to evaluate when given proper arguments

SiegelTheta often returns error messages when I give it arguments that should be of the correct form. For instance, I have a numerical matrix like ...
3
votes
0answers
147 views

Why doesn't Log[Gamma[]] simplify to LogGamma[] where it could?

I have been playing with various equations involving amount of permutations in relatively large sets. Easiest way to look at these is something like Log[10, bignumber!] . Often expressions, even ...
2
votes
0answers
88 views

Power::infy: error using FindFit

I have a 2D data to fit (the Airy type pattern from diffraction of Gaussian beam on the circular aperture). Please see the attached picture. I was going to use a function like ...
2
votes
0answers
136 views

Real integral evaluating as indeterminate

Mathematica evaluates the following integral as: ...
2
votes
0answers
90 views

RSolve and incomplete gamma function

I am interested in how Mathematica uses the incomplete gamma function to solve difference equations. For example, if we have this inhomogeneous, 2nd order equation and use ...
1
vote
0answers
99 views

Spherical harmonic derivative

Consider the following substitution Derivative[2, 0][S][th, ph] /. S -> Function[{th, ph}, SphericalHarmonicY[3, 0, th, ph]] which gives correct answer. While ...
1
vote
0answers
105 views

Minimizing a functional takes forever

I need help with minimizing a functional in Mathematica. I have a function $V(\xi)=\sum_{i=1}^\infty C_{3_i}J_0(\xi/C_i)+C_{4_i}Y_0(\xi/C_i),~~~\Sigma\leq\xi\leq\xi_1$, and want to find such ...
1
vote
0answers
124 views

How to prevent simplification of hypergeometric functions resulting from integrations?

Definite integrals from 0 to Infinity over a product of two hypergeometric (including exponential, trigonometric, hyperbolic, ...
0
votes
0answers
26 views

NonlinearModelFit::nrlnum error using FindFit /NonlinearModelFit

My question is related to my previous post I'm trying to fit experimental data (after suggestion here by David) with Airy type function `data01 = Import["366.0000cm_660.0000nm.png"]; data02 = ...