Tagged Questions
2
votes
0answers
47 views
5
votes
1answer
82 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:
$$ H_m^{(1)}(z) =\frac{i^{-m}}{\pi}\int_{-\pi/2 + i \infty}^{\pi/2 - i \infty} \exp[i m ...
11
votes
2answers
209 views
What kind of hypergeometric function is it?
I found a formula for an integral of a product of three Bessel functions at The Wolfram Functions Site:
I cannot understand what kind of hypergeometric function it is.
The Mathematica code given ...
7
votes
1answer
91 views
How to calculate this integral? Integrate[BesselJ[0, x - BesselJZero[0, 1]]/x, {x, -Infinity, Infinity}]
I tried to calculate the following integral, but it returned unevaluated.
...
5
votes
2answers
137 views
Why does Integrate return a solution that is not defined at a particular point when it actually is well defined at that point?
I am trying to compute
Integrate[Sqrt[x^4 + (y - y^2)^2], {x, 0, y}]
Mathematica 8 gives
...
5
votes
2answers
114 views
Mathematica cannot calculate a limit
When I evaluate
Limit[E^(-n)*Sum[n^k/(k!),{k,0,n}], n -> ∞]
Mathematica gives me the result
...
1
vote
0answers
75 views
Getting poles of a Gamma functions
Why do the following 2 sequences give different answers?
n = 1.5
Series[Gamma[0.5 - n - x], {x, 0, 2}]
Series[Gamma[-1 - x], {x, 0, 2}]
(..clearly the output from the second expression is ...
0
votes
2answers
214 views
Using Mathematica to find poles of Gamma functions [closed]
I am concerned about the expression on the RHS of equation A.5 (page 19) in this paper:
$$\int\frac{d^d ...
1
vote
0answers
110 views
A curious double zeta evaluation [closed]
While investigating the evaluation of a double Euler sum (a.k.a. a double zeta function),
$$\zeta(r,s)=\sum_{j=1}^\infty \sum_{k=1}^{j-1}\frac1{j^s k^r}$$
in Mathematica, I chanced upon most ...
12
votes
1answer
237 views
Extra factors appear when evaluating Euler integrals
When I perform the double integral in Mathematica,
Integrate[(x (1 - x))^z (y (1 - y))^z, {x, 0, 1}, {y, 0, 1}]
which should give
$$B(z+1,z+1)^2 = ...
3
votes
2answers
221 views
11
votes
1answer
440 views
Incorrect results for elementary integrals when using Integrate
There is a rather simple integral ($K_0$ is the 0-th order MacDonald function)
$$\int_0^\infty e^{-x \cosh\xi}\, d\xi = K_0(x)$$
which mathematica cannot solve. This even though the documentation ...
6
votes
1answer
430 views
Hankel Transform integrals won't work in Mathematica
I'm trying to do this integral, which is shown on the Wikipedia page on the Hankel transformation:
$$\int_0^{2\pi}\mathrm d\varphi\;e^{\mathrm im\varphi}e^{\mathrm ikr\cos(\varphi)}$$
The answer is ...
