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Results tagged with ca.classical-analysis-and-odes
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user 8955
Special functions, orthogonal polynomials, harmonic analysis, ordinary differential equations (ODE's), differential relations, calculus of variations, approximations, expansions, asymptotics.
1
vote
Accepted
For what values of the parameter does this function have an elementary anti-derivative?
Hi,
Your integral is the incomplete beta function, and has elementary expressions when $r$ is equal to an integer or half-integer. For example, you found the value for $r=1/2$, and when $r=3$ it is
…
- 1,077
3
votes
0
answers
672
views
Mathematica package for obtaining hypergeometric function
In my current research in electromagnetics I am encountering integrals of the form $$ \int_0^\infty dt J_0( r t) \frac{\exp(-h \sqrt{t^2 - a^2})}{\sqrt{t^2 - b^2}} t . $$ $a$ and $b$ are complex numb …
- 1,077
3
votes
An integral that somehow equals pi^2/6 and involves dilogarithms?
This problem can also be approached by rewriting the sum. I'll show a lot of details, probably too many, here.
Use the binomial series to write
$ \frac{1}{(1+x^k)^2} = \sum_{m=0}^{\infty} \binom{m+1 …
- 1,077