New Results for Srivastava's λ-Generalized Hurwitz-Lerch Zeta Function

作者：Luo, Min-Jie^*; Raina, R. K.

来源：Filomat, 2017, 31(8): 2219-2229.

DOI：10.2298/FIL1708219L

• Abel's summation formula
• Srivastava's lambda-generalized Hurwitz-Lerch Zeta function
• Kratzel function
• Mathieu (a, lambda)-series
• Two-sided inequalities

In view of the relationship with the Kratzel function, we derive a new series representation for the lambda-generalized Hurwitz-Lerch Zeta function introduced by H.M. Srivastava [Appl. Math. Inf. Sci. 8 (2014) 1485-1500] and determine the monotonicity of its coefficients. An integral representation of the Mathieu (a,lambda)-series is rederived by applying the Abel's summation formula (which provides a slight modification of the result given by Pogany [Integral Transforms Spec. Funct. 16 (8) (2005) 685-689]) and this modified form of the result is then used to obtain a new integral representation for Srivastava's lambda-generalized Hurwitz-Lerch Zeta function. Finally, by making use of the various results presented in this paper, we establish two sets of two-sided inequalities for Srivastava's lambda-generalized Hurwitz-Lerch Zeta function.

• 出版日期2017
• 单位华东师范大学