Partial Sums of Generalized Class of Analytic Functions Involving Hurwitz-Lerch Zeta Function

Murugusundaramoorthy, G.; Uma, K.; Darus, M.

Partial Sums of Generalized Class of Analytic Functions Involving Hurwitz-Lerch Zeta Function

G. Murugusundaramoorthy, K. Uma and M. Darus

Abstract and Applied Analysis, 2011, vol. 2011, 1-9

Abstract:

Let ð ‘“ ð ‘› âˆ‘ ( ð ‘§ ) = ð ‘§ + ð ‘› ð ‘˜ = 2 ð ‘Ž ð ‘˜ ð ‘§ ð ‘˜ be the sequence of partial sums of the analytic function âˆ‘ ð ‘“ ( ð ‘§ ) = ð ‘§ + âˆž ð ‘˜ = 2 ð ‘Ž ð ‘˜ ð ‘§ ð ‘˜ . In this paper, we determine sharp lower bounds for â„œ { ð ‘“ ( ð ‘§ ) / ð ‘“ ð ‘› ( ð ‘§ ) } , â„œ { ð ‘“ ð ‘› ( ð ‘§ ) / ð ‘“ ( ð ‘§ ) } , â„œ { ð ‘“ î…ž ( ð ‘§ ) / ð ‘“ î…ž ð ‘› ( ð ‘§ ) } , and â„œ { ð ‘“ î…ž ð ‘› ( ð ‘§ ) / ð ‘“ î…ž ( ð ‘§ ) } . The usefulness of the main result not only provides the unification of the results discussed in the literature but also generates certain new results.

Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:849250

DOI: 10.1155/2011/849250

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