# zbMATH — the first resource for mathematics

##### Examples
 Geometry Search for the term Geometry in any field. Queries are case-independent. Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact. "Topological group" Phrases (multi-words) should be set in "straight quotation marks". au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted. Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff. "Quasi* map*" py: 1989 The resulting documents have publication year 1989. so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14. "Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic. dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles. py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses). la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

##### Operators
 a & b logic and a | b logic or !ab logic not abc* right wildcard "ab c" phrase (ab c) parentheses
##### Fields
 any anywhere an internal document identifier au author, editor ai internal author identifier ti title la language so source ab review, abstract py publication year rv reviewer cc MSC code ut uncontrolled term dt document type (j: journal article; b: book; a: book article)
Two-sided inequalities for the extended Hurwitz-Lerch zeta function. (English) Zbl 1228.11137
Summary: Recently, the authors [Integral Transforms Spec. Funct. 22, No. 7, 487–506 (2011; Zbl 05956964)] unified and extended several interesting generalizations of the familiar Hurwitz-Lerch zeta function ${\Phi }\left(z,s,a\right)$ by introducing a Fox-Wright type generalized hypergeometric function in the kernel. For this newly introduced special function, two integral representations of different kinds are investigated here by means of a known result involving a Fox-Wright generalized hypergeometric function kernel, which was given earlier in [loc. cit], and by applying some Mathieu $\left(\alpha ,\lambda \right)$-series techniques. Finally, by appealing to each of these two integral representations, two sets of two-sided bounding inequalities are proved, thereby extending and generalizing the recent work by the last three authors [Appl. Math. Lett. 24, No. 8, 1473–1476 (2011; Zbl 1228.11135)].
##### MSC:
 11M35 Hurwitz and Lerch zeta functions 30D15 Special classes of entire functions; growth estimates 33B15 Gamma, beta and polygamma functions 33C20 Generalized hypergeometric series, ${}_{p}{F}_{q}$