Identities for the Hurwitz zeta function, Gamma function, and L-functions
| Autor: | Michael O. Rubinstein |
|---|---|
| Rok vydání: | 2013 |
| Předmět: |
Pure mathematics
Algebra and Number Theory Polylogarithm Mathematics - Number Theory Mathematics::Number Theory Riemann zeta function Bernoulli polynomials Hurwitz zeta function Algebra symbols.namesake Arithmetic zeta function 11M06 Digamma function Multiplication theorem FOS: Mathematics symbols Number Theory (math.NT) Dirichlet series Mathematics |
| Zdroj: | The Ramanujan Journal. 32:421-464 |
| ISSN: | 1572-9303 1382-4090 |
| DOI: | 10.1007/s11139-013-9468-0 |
| Popis: | We derive several identities for the Hurwitz and Riemann zeta functions, the Gamma function, and Dirichlet L-functions. They involve a sequence of polynomials α k (s) whose study was initiated in Rubinstein (Ramanujan J. 27(1): 29–42, 2012). The expansions given here are practical and can be used for the high precision evaluation of these functions, and for deriving formulas for special values. We also present a summation formula and use it to generalize a formula of Hasse. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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