Expansions of the solutions of the confluent Heun equation in terms of the incomplete Beta and the Appell generalized hypergeometric functions
| Affiliation auteurs | Affiliation ok |
| Titre | Expansions of the solutions of the confluent Heun equation in terms of the incomplete Beta and the Appell generalized hypergeometric functions |
| Type de publication | Journal Article |
| Year of Publication | 2015 |
| Auteurs | Leroy C., Ishkhanyan A.M |
| Journal | INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS |
| Volume | 26 |
| Pagination | 451-459 |
| Date Published | JUN 3 |
| Type of Article | Article |
| ISSN | 1065-2469 |
| Mots-clés | 30Bxx Series expansions, 33E30 Other functions coming from differential, 34B30 Special equations (Mathieu, Bessel, confluent Heun equation, difference and integral equations, etc.), Hill, linear ordinary differential equation, recurrence relations, series expansions, special functions |
| Résumé | We construct several expansions of the solutions of the confluent Heun equation in terms of the incomplete Beta functions and the Appell generalized hypergeometric functions of two variables of the first kind. The coefficients of different expansions obey four-, five-, or six-term recurrence relations that are reduced to ones involving less number of terms only in a few exceptional cases. The conditions for deriving finite-sum solutions via termination of the series are discussed. |
| DOI | 10.1080/10652469.2015.1019490 |