New posts in bessel-functions

How to prove that $ \mathcal{L}[J_0(\sqrt {t^2+2t})] = \frac {e^{ \sqrt {s^2+1}}}{\sqrt{s^2+1}} $

integration laplace-transform gamma-function bessel-functions

Closed form of $\sum_{n=1}^{\infty} \frac{J_0(2n)}{n^2}$

calculus integration sequences-and-series definite-integrals bessel-functions

$ y' = x^2 + y^2 $ asymptote

ordinary-differential-equations bessel-functions

Verify $y=x^aZ_p\left(bx^c\right)$ is a solution to $y''+\left(\frac{1-2a}{x}\right)y'+\left[(bcx^{c-1})^2+\frac{a^2-p^2c^2}{x^2}\right]y=0$

ordinary-differential-equations derivatives special-functions proof-explanation bessel-functions

Integral representation of $\sum_{k=0}^{n} \frac{x^k}{(k!)^2}$?

summation asymptotics bessel-functions

Asymptotic form of Bessel $Y_0(x)$ for small $x$

asymptotics improper-integrals bessel-functions

$\sum _{m=0}^{\infty} \frac{b^m }{(m!)^2}K_{m+\frac{1}{2}}(a)$ with Bessel K

sequences-and-series bessel-functions

Proving that $\int_0^\infty\frac{J_{2a}(2x)~J_{2b}(2x)}{x^{2n+1}}~dx~=~\frac12\cdot\frac{(a+b-n-1)!~(2n)!}{(n+a+b)!~(n+a-b)!~(n-a+b)!}$

calculus integration definite-integrals closed-form bessel-functions

For $a>0$, what is $\int_1^\infty dy \, \exp(-ay) (y^2-1)^{-1/2}y^{-2}$?

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

What is $\lim\limits_{n\to\infty} (\text j_{x,x}-\text y_{x,x})$ with the BesselYZero and BesselJZero function?

limits roots special-functions bessel-functions constants

Is there any meaning to this "Super Derivative" operation I invented?

derivatives gamma-function bessel-functions fractional-calculus

Modified Bessel function near zero

integration asymptotics bessel-functions

What are BesselJ functions?

real-analysis integration analysis special-functions bessel-functions