Some functional relations derived from the Lindelöf-Wirtinger expansion of the Lerch transcendent function
-
1
Universidad de Salamanca
info
-
2
Universidad de Zaragoza
info
-
3
Universidad de La Rioja
info
ISSN: 0025-5718
Datum der Publikation: 2015
Ausgabe: 84
Nummer: 292
Seiten: 803-813
Art: Artikel
Andere Publikationen in: Mathematics of Computation
Projekte im Zusammenhang
Zusammenfassung
The Lindelöf-Wirtinger expansion of the Lerch transcendent function implies, as a limiting case, Hurwitz's formula for the eponymous zeta function. A generalized form of Möbius inversion applies to the Lindelöf-Wirtinger expansion and also implies an inversion formula for the Hurwitz zeta function as a limiting case. The inverted formulas involve the dynamical system of rotations of the circle and yield an arithmetical functional equation.