2
votes
1answer
73 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 ...
1
vote
1answer
107 views

How to calculate the following integral of the multiplication of two Bessel functions?

This integration has an analytical solution and its behavior is described by 1/r^2 function, but Mathematica gives some weird oscillating answer. Can anybody explain this and help me overcome this ...
3
votes
1answer
271 views

A Bessel & Struve functions related integral

I try to numerically compute this integral and I don't figure out why on earth Mathematica is not able to do it. Is my input correct? Does it possibly have a closed form? ...
1
vote
1answer
105 views

Numerical integration of Hankel functions

I would like to know how to perform numeric integration for the following type of integrals in Mathematica. For the following integrand, we can not get the symbolic result. ...
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 ...
7
votes
1answer
320 views

Numerical contour integrations in the complex plane - contour deformation gives different answer for analytic kernel

I am trying to do a contour integration in Mathematica numerically. In particular, I'm checking the identity: $$ H_m^{(1)}(z) =\frac{i^{-m}}{\pi}\int_{-\pi/2 + i \infty}^{\pi/2 - i \infty} \exp[i m ...
9
votes
1answer
434 views

Why can't I change the value of MaxRecursion in NIntegrate when integrating BesselJ?

I am trying to evaluate this integral numerically $$ \int_0^{\infty } J_0(q R) \tanh(q) \, \mathrm{d}q $$ for large values of $R$. This makes the integrand oscillate more quickly and Mathematica ...
7
votes
2answers
284 views

Problem with NIntegrate when WorkingPrecision is specified

I am trying to evaluate this integral numerically: $$ \int_0^{\infty } m \exp (-m) J_1(m){}^2 \, dm $$ Everything is OK when only the integration method is specified: ...
6
votes
2answers
254 views

Cannot Get Numerical Results to Match

I try this numerical summation (in two parts) ...
2
votes
1answer
236 views

Directional derivative of SiegelTheta

I'm working on a problem where I have to integrate both the Mathematica function SiegelTheta and some of its second order directional derivatives. Using the function works well but something goes ...
4
votes
2answers
163 views

LevinRule and SphericalBessels

I'm currently looking at a simplified problem that approximates another problem I'm looking into. In this simplified problem I at least have an analytic integrand and can easily provide all info on ...