New posts in bessel-functions

Proof $\int_0^\infty \frac{\exp(-\sqrt{x^2+y^2})}{x^2+y^2}dx = \frac{\pi}{2}\left(\frac{1}{y} - K_0(y)L_{-1}(y) - K_1(y)L_{0}(y)\right)$

definite-integrals improper-integrals bessel-functions

Sup norm of Fourier transform of $ \frac{\sin |x|}{|x|^\lambda} \mathbb 1_{\{2^k\le |x| <2^{k+1}\}}, \ 0<\lambda<n $

functional-analysis fourier-analysis fourier-transform harmonic-analysis bessel-functions

Double integral with Hankel transform

integration bessel-functions integral-transforms

Integral representation of Bessel function $J_1(x)$

integration improper-integrals bessel-functions absolute-convergence conditional-convergence

Accurate identities related to $\sum\limits_{n=0}^{\infty}\frac{(2n)!}{(n!)^3}x^n$ and $\sum\limits_{n=0}^{\infty}\frac{(2n)!}{(n!)^4}x^n$

calculus sequences-and-series laplace-transform bessel-functions elliptic-integrals

Asymptotic Expansion of the Bessel-Integral Function

asymptotics bessel-functions

Integral ${\large\int}_0^\infty\big(2J_0(2x)^2+2Y_0(2x)^2-J_0(x)^2-Y_0(x)^2\big)\,dx$

integration definite-integrals special-functions closed-form bessel-functions

Asymptotic answer of Fourier transform radially symmetric function with a ring of minimum

integration asymptotics fourier-transform bessel-functions

Determining when $\int_{0}^{\infty} \cos(\alpha x) \prod_{m=1}^{n} J_{0}(\beta_{m} x) \, \mathrm dx =0$ without using contour integration

integration complex-analysis improper-integrals bessel-functions

Limit of integral with a Bessel function

integration limits bessel-functions

Difficult infinite integral involving a Gaussian, Bessel function and complex singularities

integration definite-integrals special-functions bessel-functions

How to evaluate the Fourier Series of $\frac{\sin(\alpha\sin(\omega t))}{\alpha\sin(\omega t)}\exp(-j\beta\sin(\omega t))$?

definite-integrals fourier-series bessel-functions

Solve $\int_0^{2\pi} \cos(a\cos(x) + b\sin(x) + cx + d)dx$

integration definite-integrals bessel-functions

The integral of the product of a Bessel function and a trigonometric function $\int J_0(x)\sin(ax)\mathrm{d}x$

integration bessel-functions

Delta-function representations, Bessel function

integration sequences-and-series dirac-delta bessel-functions

Proving an integral is finite

real-analysis integration asymptotics estimation bessel-functions

On the integral $\int_{(0,1)^n}\frac{\prod\sin\theta_k}{\sum\sin\theta_k}d\mu$

definite-integrals special-functions bessel-functions hypergeometric-function

Prove known closed form for $\int_0^\infty e^{-x}I_0\left(\frac{x}{3}\right)^3\;dx$

definite-integrals closed-form gamma-function bessel-functions elliptic-integrals

Integrals of the Bessel function $J_0(x)$ over the intervals between its zeros

real-analysis integration asymptotics bessel-functions conjectures

Calculation of Bessel Functions

sequences-and-series algorithms numerical-methods bessel-functions