On extended Hurwitz–Lerch zeta function
| Autor: | Rakesh K. Parmar, Ravinder Krishna Raina, Min-Jie Luo |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Pure mathematics
Series (mathematics) Applied Mathematics Multiple integral 010102 general mathematics Mathematical analysis Generating function Monotonic function Function (mathematics) 01 natural sciences Riemann zeta function 010101 applied mathematics symbols.namesake Lerch zeta function symbols Abel's summation formula 0101 mathematics Analysis Mathematics |
| Zdroj: | Journal of Mathematical Analysis and Applications. 448:1281-1304 |
| ISSN: | 0022-247X |
| DOI: | 10.1016/j.jmaa.2016.11.046 |
| Popis: | This paper investigates an extended form of a beta function B p , q ( x , y ) . We first study the convergence problem of the function B p , q ( x , y ) and consider the completely monotonic and log-convex properties of this function. As a result, we obtain a pair of Laguerre type inequalities. Next, we provide a new double integral representation for the function B p , q ( x , y ) . Subsequently, we consider the convergence problem of the extended Hurwitz–Lerch zeta function Φ λ , μ ; ν ( z , s , a ; p , q ) defined by its series representation. Upon using the series manipulation techniques, we obtain two series identities. We also find various integral representations for the function Φ λ , μ ; ν ( z , s , a ; p , q ) . Lastly, we apply Fourier analysis to the function z a Φ μ ; ν ( z , s , a ; p , q ) and obtain a Lindelof–Wirtinger type expansion. Some interesting and promising results are also illustrated. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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