Questions tagged [special-functions]
For questions about evaluating or implementing special functions, e.g. Bessel, hypergeometric, gamma, Lambert W.
7
questions with no upvoted or accepted answers
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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 ...
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5
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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 ...
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2
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Best way to compute given functional with accuracy:
I need to plot the following functional with accuracy:
$$
I(x,s) =\int_0^\infty\mathrm dy \frac{F(x + \mathrm iy,s) − F(x −\mathrm iy,s)}{\mathrm e^{2πy}-1},
$$
Where $ F(z,s) = \dfrac{1}{z^s\Gamma(\...
- 119
2
votes
0
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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 ...
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2
votes
0
answers
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Accurate computation of $\frac{\mathrm{B}_{x,y}(\alpha + 1,\beta)}{\mathrm{B}_{x,y}(\alpha,\beta)}$ for large paramers?
I need to calculate these ratios:
$$\frac{\mathrm{B}_{x,y}(\alpha + 1,\beta)}{\mathrm{B}_{x,y}(\alpha,\beta)} \tag{1}$$
where $\alpha,\beta > 0$ and $0\le x\le y \le 1$. Here $\mathrm{B}_{x,y}(\...
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1
vote
0
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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
1
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0
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Using Spherical Bessel Functions in Python
My question relates to using spherical Bessel functions in Python.
If my ODE contains a spherical Bessel function of the form $$j_\ell(tx)$$ and similarly $$y_\ell(tx)$$
for given values of $t$ and $...
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