{"docId":150,"paperId":150,"url":"https:\/\/hrj.episciences.org\/150","doi":"10.46298\/hrj.2004.150","journalName":"Hardy-Ramanujan Journal","issn":"","eissn":"2804-7370","volume":[{"vid":38,"name":"Volume 27 - 2004"}],"section":[],"repositoryName":"Hal","repositoryIdentifier":"hal-01110916","repositoryVersion":1,"repositoryLink":"https:\/\/hal.archives-ouvertes.fr\/hal-01110916v1","dateSubmitted":"2015-03-03 16:13:56","dateAccepted":"2015-06-12 16:05:48","datePublished":"2004-01-01 08:00:00","titles":{"en":"A generalization of Bochner's formula"},"authors":["Kanemitsu, S","Tanigawa, Y","Tsukada, H"],"abstracts":{"en":"In this note we expound our general hierarchy theorems by the example of a Ramified-Type Functional Equarion H, which gives all possbile forms, in terms of se-ries with H-function coefficients, of the functional equation of higher hierarchy arising from the original ramified one satisfied by the Dirichlet series. Then by sepcifying the parameters, we shall deduce a few concrete examples scattered in the literature in the most natural way."},"keywords":[{"en":"zeta-function"},{"en":" generalised Hurwitz-Lerch zeta-function"},{"en":" ramified-type functional equation"},{"en":" Fox $H$-function"},{"en":" Bochner's formula"},"[MATH] Mathematics [math]"]}