Some Difference Equations for Srivastava’s λ-Generalized Hurwitz–Lerch Zeta Functions with Applications
Abstract
:1. Introduction
2. Results
3. Some applications of the difference equation
4. Integrals of products of the family of λ-Generalized Hurwitz–Lerch zeta functions
5. Discussion and Future Directions
Funding
Acknowledgments
Conflicts of Interest
References
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λ-Generalized Hurwitz–Lerch Zeta Functions | [1], (p. 1487), Equation (1.14) | [41], (p. 90), Equation (6) and [42] | ([1], p. 1486, Equation (1.11)) & [2] | ([43], p. 100, Equation (1.5)) | ([44], p. 27, Equation (1.11)) | |||
λ-Generalized Extended Fermi–Dirac and Extended Bose–Einstein Functions | ([43], p. 12, Equation (45)) | ([45], p. 9, Equation (3.14)) | ||||||
([43], p. 12, Equation (45)) | [45], p. 115, Equation (4.4) | |||||||
λ-Generalized Polylogarithm Functions | ([43], p. 12, Equation (47)) | [44], (Chapter 1) | ||||||
λ-Generalized Fermi–Dirac and Bose–Einstein Functions | ([43], p. 12, Equation (47)) | ([45], p. 109, Equation (1.12) | ||||||
([43], p. 12, Equation (45)) | ([45], p. 109, Equation (1.12)) | |||||||
λ-Generalized Hurwitz zeta Functions | [46], p. 308 | [43] | [44], (Chapter 1) | |||||
λ-Generalized Riemann Zeta Functions | [46], p. 308 | [43] | [44], (Chapter 1) |
s | Direct Evaluation by Mathematica | Using difference Equation (34) |
---|---|---|
4 | ||
30 | ||
40 | ||
45 | ||
46 | ||
48 | ||
48.5 | ||
48.9 | ||
49 | ||
52 | ||
56 | ||
160 | Unable to compute | |
220 | Unable to compute | |
400 | Unable to compute |
s | Direct Evaluation by Mathematica | By using difference Equation (40) |
---|---|---|
90 | ||
100 | ||
140 | Unable to compute | |
160 | Unable to compute |
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Tassaddiq, A. Some Difference Equations for Srivastava’s λ-Generalized Hurwitz–Lerch Zeta Functions with Applications. Symmetry 2019, 11, 311. https://doi.org/10.3390/sym11030311
Tassaddiq A. Some Difference Equations for Srivastava’s λ-Generalized Hurwitz–Lerch Zeta Functions with Applications. Symmetry. 2019; 11(3):311. https://doi.org/10.3390/sym11030311
Chicago/Turabian StyleTassaddiq, Asifa. 2019. "Some Difference Equations for Srivastava’s λ-Generalized Hurwitz–Lerch Zeta Functions with Applications" Symmetry 11, no. 3: 311. https://doi.org/10.3390/sym11030311