A generalization of Bochner's formula

S Kanemitsu (1) , Y Tanigawa (2) , H Tsukada (1)

1 University ok Kinki
2 Graduate School of Mathematics [Nagoya]

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.

Mots clés: zeta-function; generalised Hurwitz-Lerch zeta-function; ramified-type functional equation; Fox $H$-function; Bochner's formula

Domaines: Mathématiques [math]

S Kanemitsu, Y Tanigawa, H Tsukada. A generalization of Bochner's formula. Hardy-Ramanujan Journal, 2004, Volume 27 - 2004, pp.28-46. ⟨10.46298/hrj.2004.150⟩. ⟨hal-01110916⟩