Functional Equation

Antanas Laurinčikas and Ramūnas Garunkštis
Additional contact information
Antanas Laurinčikas: Vilnius University
Ramūnas Garunkštis: Vilnius University

Chapter Chapter 2 in The Lerch Zeta-function, 2003, pp 17-30 from Springer

Abstract: Abstract Let λ ∈ ℝ and 0 L ( λ , α , s ) = ∑ m = 0 ∞ e 2 π i λ m ( m + α ) s . $$L\left( {\lambda ,\alpha ,s} \right) = \sum\limits_{m = 0}^\infty {\frac{{e^{2\pi i\lambda m} }} {{\left( {m + \alpha } \right)^s }}.}$$ for σ > 1 if λ ∈ ℤ, and for σ > 0 if λ ∉ ℤ. For λ ∈ ℤ the Lerch zeta-function reduces to the Hurwitz zeta-function ζ(s, α): ζ ( s , a ) = ∑ m = 0 ∞ 1 ( m + a ) s , σ > 1. $$\zeta \left( {s,a} \right) = \sum\limits_{m = 0}^\infty {\frac{1}{{{{\left( {m + a} \right)}^s}}},\;\sigma > 1.} $$

Date: 2003
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-017-6401-8_2

Ordering information: This item can be ordered from
http://www.springer.com/9789401764018

DOI: 10.1007/978-94-017-6401-8_2

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().