Reflection formulas for order derivatives of Bessel functions

From new integral representations of the $n$-th derivative of Bessel functions with respect to the order, we derive some reflection formulas for the first and second order derivative of $J_{\nu }\left( t\right)$ and % Y_{\nu }\left( t\right) for integral order, and for the $n$-th order derivative of $I_{\nu }\left( t\right)$ and $K_{\nu }\left( t\right)$ for arbitrary real order. As an application of the reflection formulas obtained for the first order derivative, we extend some formulas given in the literature to negative integral order. Also, as a by-product, we calculate an integral which does not seem to be reported in the literature.Comment: arXiv admin note: text overlap with arXiv:1808.0560

Geometries of orthogonal groups and their contractions: a unified classical deformation viewpoint

The geometries of spaces having as groups the real orthogonal groups and some of their contractions are described from a common point of view. Their central extensions and Casimirs are explicitly given. An approach to the trigonometry of their spaces is also advanced.Comment: 9 pages, LaTeX; contribution presented by M.Santander to the II International Workshop on Classical and Quantum Integrible Systems (Dubna, 8-12 July,1996), to be published in Int.J.Mod.Phys.