Some Difference Equations for Srivastava’s λ-Generalized Hurwitz–Lerch Zeta Functions with Applications
In this article, we establish some new difference equations for the family of λ-generalized Hurwitz–Lerch zeta functions. These difference equations proved worthwhile to study these newly defined functions in terms of simpler functions. Several authors investigated such function...
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| Format: | Article |
| Language: | English |
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MDPI AG
2019-03-01
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| Series: | Symmetry |
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| Online Access: | http://www.mdpi.com/2073-8994/11/3/311 |
| _version_ | 1798005450686332928 |
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| author | Asifa Tassaddiq |
| author_facet | Asifa Tassaddiq |
| author_sort | Asifa Tassaddiq |
| collection | DOAJ |
| description | In this article, we establish some new difference equations for the family of λ-generalized Hurwitz–Lerch zeta functions. These difference equations proved worthwhile to study these newly defined functions in terms of simpler functions. Several authors investigated such functions and their analytic properties, but no work has been reported for an estimation of their values. We perform some numerical computations to evaluate these functions for different values of the involved parameters. It is shown that the direct evaluation of involved integrals is not possible for the large values of parameter s; nevertheless, using our new difference equations, we can evaluate these functions for the large values of s. It is worth mentioning that for the small values of this parameter, our results are 100% accurate with the directly computed results using their integral representation. Difference equations so obtained are also useful for the computation of some new integrals of products of λ-generalized Hurwitz–Lerch zeta functions and verified to be consistent with the existing results. A derivative property of Mellin transforms proved fundamental to present this investigation. |
| first_indexed | 2024-04-11T12:39:26Z |
| format | Article |
| id | doaj.art-fe92a8f642c447deab53d450b675a3b2 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-04-11T12:39:26Z |
| publishDate | 2019-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-fe92a8f642c447deab53d450b675a3b22022-12-22T04:23:32ZengMDPI AGSymmetry2073-89942019-03-0111331110.3390/sym11030311sym11030311Some Difference Equations for Srivastava’s λ-Generalized Hurwitz–Lerch Zeta Functions with ApplicationsAsifa Tassaddiq0College of Computer and Information Sciences Majmaah University, Al Majmaah 11952, Saudi ArabiaIn this article, we establish some new difference equations for the family of λ-generalized Hurwitz–Lerch zeta functions. These difference equations proved worthwhile to study these newly defined functions in terms of simpler functions. Several authors investigated such functions and their analytic properties, but no work has been reported for an estimation of their values. We perform some numerical computations to evaluate these functions for different values of the involved parameters. It is shown that the direct evaluation of involved integrals is not possible for the large values of parameter s; nevertheless, using our new difference equations, we can evaluate these functions for the large values of s. It is worth mentioning that for the small values of this parameter, our results are 100% accurate with the directly computed results using their integral representation. Difference equations so obtained are also useful for the computation of some new integrals of products of λ-generalized Hurwitz–Lerch zeta functions and verified to be consistent with the existing results. A derivative property of Mellin transforms proved fundamental to present this investigation.http://www.mdpi.com/2073-8994/11/3/311analytic number theoryλ-generalized Hurwitz–Lerch zeta functionsderivative propertiesrecurrence relationsintegral representationsMellin transform |
| spellingShingle | Asifa Tassaddiq Some Difference Equations for Srivastava’s λ-Generalized Hurwitz–Lerch Zeta Functions with Applications Symmetry analytic number theory λ-generalized Hurwitz–Lerch zeta functions derivative properties recurrence relations integral representations Mellin transform |
| title | Some Difference Equations for Srivastava’s λ-Generalized Hurwitz–Lerch Zeta Functions with Applications |
| title_full | Some Difference Equations for Srivastava’s λ-Generalized Hurwitz–Lerch Zeta Functions with Applications |
| title_fullStr | Some Difference Equations for Srivastava’s λ-Generalized Hurwitz–Lerch Zeta Functions with Applications |
| title_full_unstemmed | Some Difference Equations for Srivastava’s λ-Generalized Hurwitz–Lerch Zeta Functions with Applications |
| title_short | Some Difference Equations for Srivastava’s λ-Generalized Hurwitz–Lerch Zeta Functions with Applications |
| title_sort | some difference equations for srivastava s λ generalized hurwitz lerch zeta functions with applications |
| topic | analytic number theory λ-generalized Hurwitz–Lerch zeta functions derivative properties recurrence relations integral representations Mellin transform |
| url | http://www.mdpi.com/2073-8994/11/3/311 |
| work_keys_str_mv | AT asifatassaddiq somedifferenceequationsforsrivastavaslgeneralizedhurwitzlerchzetafunctionswithapplications |