New posts in bessel-functions

Closed form of integral over fractional part $\int_0^1 \left\{\frac{1}{2}\left(x+\frac{1}{x}\right)\right\}\,dx$

integration summation asymptotics bessel-functions fractional-part

Can $ I_n(z) = (\frac{z}{2})^n\sum_{k=0}^\infty\frac{(-1)^k}{k!(n+k)!}\frac{1}{k+(n+k)+1}(\frac{z}{2})^{2k}$ be expressed by the Bessel function?

taylor-expansion bessel-functions

Bound/inequality for Hankel function

inequality bessel-functions

How to solve integral $\int_0^{2\pi} e^{i(a\cos\phi + b\sin\phi)} \cos\phi\ d\phi$

integration definite-integrals bessel-functions

Conjecture $\sum_{m=1}^\infty\frac{y_{n+1,m}y_{n,k}}{[y_{n+1,m}-y_{n,k}]^3}\overset{?}=\frac{n+1}{8}$, where $y_{n,k}=(\text{BesselJZero[n,k]})^2$

sequences-and-series special-functions closed-form bessel-functions conjectures

Bessel's Differential Equation - textbook queries:

ordinary-differential-equations recurrence-relations special-functions bessel-functions

$\int^{2\pi}_0 i\sin(x\sin \theta -n\theta) d\theta$

complex-analysis analysis bessel-functions

Prove that $ \sum_{k=0}^n \frac{(-1)^k}{k!}\binom{n}{k}=e\int_0^\infty \frac{t^ne^{-t}}{n!} J_0(2\sqrt{t})\;\mathrm{d}t$ using only real analysis.

real-analysis integration sequences-and-series binomial-coefficients bessel-functions

$\int_{-\pi}^\pi e^{-\sin^2(x) - A\sin^2(nx)}dx$ for an integer n

integration definite-integrals bessel-functions

Show the equivalence of two infinite series over Bessel functions

sequences-and-series special-functions bessel-functions

How to use Chebyshev Polynomials to approximate $\sin(x)$ and $\cos(x)$ within the interval $[−π,π]$?

trigonometry taylor-expansion bessel-functions chebyshev-polynomials

How to prove this Bessel equality? [closed]

bessel-functions

Simplification of a sum of Bessel functions

calculus algebra-precalculus bessel-functions

Evaluate $\sum _{n=1}^{\infty } \frac{\sin \left(x \sqrt{a^2+n^2}\right)}{\left(a^2+n^2\right)^{3/2}}$ and generalize it

sequences-and-series special-functions closed-form bessel-functions

How to integrate $\int_1^\infty e^{-\alpha x}J_0(\beta\sqrt{x^2-1})\mathrm{d}x \,$?

integration definite-integrals bessel-functions

Evaluation the Elsasser function:$\text E(y,u)=\int_{-\frac12}^\frac12e^{\frac{2\pi uy\sinh(2\pi y )}{\cos(2\pi x)-\cosh(2\pi y)}}dx$ from MathWorld

sequences-and-series definite-integrals special-functions bessel-functions trigonometric-integrals

Integral of Bessel function multiplied with sine $\int_0^\infty J_0(bx) \sin(ax) dx$.

integration definite-integrals special-functions bessel-functions

I have an equation derived from Ising model for the correlation distance. Is there a way to rewrite this integral to make in manageable?

indefinite-integrals bessel-functions

Derivation of Gradshteyn and Ryzhik integral 3.876.1 (in question)

calculus definite-integrals bessel-functions integration

Find Spherical Integral: $\int_{\| {\bf x}\|=1} x_1 e^{ {\bf x}^T{\bf y}} {\rm d} {\bf x}$

integration multivariable-calculus bessel-functions