All Questions
Tagged with integration special-functions
9 questions
1
vote
0
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77
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Computation of a functional for large values
Consider the following function :
$$f(x) = \sin^2(\frac{π\Gamma(x)}{2x})$$
Now consider the following functional :
$$I(x)=\int_0^\infty \frac{f(x + iy) − f(x − iy)}{e^{2πy}-1} dy$$
I need values for ...
- 119
2
votes
0
answers
53
views
To use the confluent hypergeometric function or not to?
I am numerically computing the following integral as a function of positive $k$.
$$I(k) := \int_0^\infty x^b(k+x)^{a-1} e^{-x} dx \tag1$$
It is shown in math.stackexchange.com that this can be ...
- 121
1
vote
3
answers
294
views
Comparison of integrals with a function:
Consider the following integral:
$$S(q)=\int_{x=2}^q\sin^2\left(\frac{π\Gamma(x)}{2x}\right)dx$$
And consider the functions :
$$R(q)=\frac{q}{\log(q)}$$
$$T(q)=\int_2^q\frac{1}{\log(x)}dx$$
I ...
- 119
0
votes
2
answers
125
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Is expm1 the right primitive?
I'm writing some code to calculate $\int_0^1 e^{ax} \mathrm{d} x$. Annoyingly there does not seem to be a way of doing this without if statements:
...
- 373
5
votes
0
answers
194
views
Best way to numerically compute elliptic integrals of the third kind with complex arguments?
I need to compute elliptic integrals of the third kind with complex arguments, preferably in C++. Is there code out there to do this? I have discovered the Arb library, but that does much more than I ...
- 201
2
votes
2
answers
812
views
Integration of a diverge function in c++ GSL Library
I am trying to perform an Integral of Hypergeometric function 2F1(a,b,c,x) from -1 to 1 for some good values of $a,b,c$ (lets say $a=1,b=2,c=3$) .
I did it in ...
7
votes
1
answer
276
views
Numerical integration of a hypergeometric function
The Task
Let $z_1, z_2, z_3$ be positive real numbers and define
$$
r(\mathbf{z}):= \int_0 ^\infty (t+z_1)^{-3/2}(t+z_2)^{-3/2}(t+z_3)^{-1/2}\text{d}t.
$$
The task is to compute $r$ numerically in ...
- 374
11
votes
0
answers
355
views
Numerical integration using interval arithmetic, nowadays
Is there now a package for rigorous numerical integration that uses interval arithmetic and has access to a well-developed library of special functions?
By "well-developed", I mean something that, at ...
- 279
8
votes
1
answer
211
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Radial integration of expensive function with Bessel weights
I need to calculate the integral
$$I = \int_0^R f(r)J_n\left(\frac{z_{nm}r}{R}\right)rdr$$
where $J_n$ is the $n^{\mathrm{th}}$ order Bessel functions of the first kind, $z_{nm}$ is its $m^{\mathrm{...
- 81