# 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
Filter by
Sorted by
Tagged with
333 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 ...
176 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 ...
160 views

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 $F(z,s) = \dfrac{1}{z^s\Gamma(\... 2 votes 0 answers 51 views ### To use the confluent hypergeometric function or not to? I am numerically computing the following integral as a function of positive$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 ... 2 votes 0 answers 69 views ### 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}(\...
1 vote
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 ...
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 \$...