Hi, let $1 < p <\infty $, $ 0 < \alpha < 1$, and $ \mathscr{L}^p_\alpha(R^n) $ be the usual Bessel potential space defined by $$ \mathscr{L}^p_\alpha = (1-\triangle)^{- …

Hello, If X and Y follow independently a density distribution represented by the function $\tfrac{1}{\pi} K_0\left(\tfrac{|x|}{a^2}\right)$ (a modified Bessel function of the seco …

Please help me prove the following identity $$ a(J_1(a)Y_0(a)-J_0(a)Y_1(a))=\frac{2}{\pi} $$ for any $a$. $J$ and $Y$ are bessel functions of the first and second kind respectively …

let be a Bessel function $ J_{u} (x) $ if both the index 'u' and the argument 'x' are complex $$ J_{ia}(ib) $$ for real 'a' and 'b' what is then the name for this function ?? i …

The Bessel Potential Space is defined for $s\in\mathbb{R}$ as, $H^s(\mathbb{R}^d) = \{f\in L_2(\mathbb{R}^n) : (1+|\cdot|)^{s/2}\hat{f}(\cdot)\in L_2(\mathbb{R}^n)\}. $ This defi …