(** This file is part of the Coquelicot formalization of real analysis in Coq: http://coquelicot.saclay.inria.fr/  Copyright (C) 2011-2015 Sylvie Boldo #<br /># Copyright (C) 2011-2015 Catherine Lelay #<br /># Copyright (C) 2011-2015 Guillaume Melquiond  This library is free software; you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License as published by the Free Software Foundation; either version 3 of the License, or (at your option) any later version.  This library is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the COPYING file for more details. *)
(** This file is an example of how to use power series. It defines and gives properties of the Bessel functions. *)
Definition Bessel1_seq (n k : nat) :=
(-1)^(k)/(INR (fact (k)) * INR (fact (n + (k)))).

(* Specifications: *)
Lemma Bessel1_seq_neq_0 (n : nat) :
forall k, Bessel1_seq n k <> 0.
Lemma CV_Bessel1 (n : nat) :
CV_radius (Bessel1_seq n) = p_infty.
Lemma ex_Bessel1 (n : nat) (x : R) :
ex_pseries (Bessel1_seq n) x.