TL;DR: In this article, Bessel et al. derive representations integrales d'integrales and derivees par rapport a l'ordre des fonctions de Bessel J v (t), I v(t), de la fonction deBessel integrale Ji v (T) and la fONction d'Auger J v(T)
Abstract: On donne des representations integrales d'integrales et de derivees par rapport a l'ordre des fonctions de Bessel J v (t), I v (t), de la fonction de Bessel integrale Ji v (t) et la fonction d'Auger J v (t)
TL;DR: In this article, an approach to infinite series of Bessel functions, exploiting a method based on a combination of the integral representation and the generating function technique, is discussed, and a connection between Newberger type series and the Anger function is made.
Abstract: In this paper we discuss an approach to infinite series of Bessel functions, exploiting a method based on a combination of the integral representation and the generating function technique. We also present a connection between Newberger type series and the Anger function.
TL;DR: In this paper, the authors consider the theory of many variable Hermite-Bessel functions and discuss their generating functions, integral representations, their link to circular functions and the associated Kapteyn series.
Abstract: We reconsider the theory of many variable Hermite–Bessel functions and discuss their generating functions, integral representations, their link to circular functions and the associated Kapteyn series.
TL;DR: Closed expressions for the Weber E ±n (z), E 1/2±n n (z) and Anger J ±n(z) functions were obtained in this article.
Abstract: Closed expressions are obtained for the Weber E ±n (z), E 1/2±n (z) and Anger J ±n (z), J 1/2±n (z) functions (n=0, 1, …), for the nth derivatives of E ν(z) and J ν(z) with respect to the argument and for the first derivatives with respect to the order ν at the points ν=±n.