Some functional relations derived from the Lindelöf-Wirtinger expansion of the Lerch transcendent function

Autor: Navas, L.M.; Ruiz, F.J.; Varona Malumbres, Juan Luis

Tipo de documento: Artículo de revista

Revista: Mathematics of Computation. ISSN: 0025-5718. Año: 2015. Número: 292. Volumen: 84. Páginas: 803-813.

Texto completo open access 

JCR (datos correspondientes al año 2014):
Edición:
Science  Área: MATHEMATICS, APPLIED  Quartil: Q1  Lugar área: 40/255  F. impacto: 1,491 

SCIMAGO (datos correspondientes al año 2014):
SJR:
1,875  SNIP: 1,76 

CIRC: GRUPO A - EXCELENCIA

Referencias:

  • Apostol, T.M., On the Lerch zeta function (1951) Pacific J. Math, 1, pp. 161-167. , MR0043843 (13,328b)
  • Apostol, T.M., Zeta and related functions (2010) NIST handbook of mathematical functions, pp. 601-616. , U.S. Dept. Commerce, Washington, DC. MR2655365
  • Balanzario, E.P., Sánchez-Ortiz, J., Riemann-Siegel integral formula for the Lerch zeta function (2012) Math. Comp, 81 (280), pp. 2319-2333. , MR2945158
  • Bayad, A., Chikhi, J., Möbius inversion formulae for Apostol-Bernoulli type polynomials and numbers (2013) Math. Comp, 82 (284), pp. 2327-2332. , MR3073203
  • Benito, M., Navas, L.M., Varona, J.L., Möbius inversion formulas for flows of arithmetic semigroups (2008) J. Number Theory, 128 (2), pp. 390-412. , MR2380327 (2009c:11160)
  • Benito, M., Navas, L.M., Varona, J.L., Möbius inversion from the point of view of arithmetical semigroup flows (2008) Proceedings of the "
  • Segundas Jornadas de Teoría de Números"
  • , Bibl. Rev. Mat. Iberoamericana, Rev. Mat. Iberoamericana, Madrid, pp. 63-81. , MR2603898 (2011e:11006)
  • Boyadzhiev, K.N., Apostol-Bernoulli functions, derivative polynomials and Eulerian polynomials (2008) Adv. Appl. Discrete Math, 1 (2), pp. 109-122. , MR2450260 (2009g:11024)
  • Erdélyi, A., Magnus, W., Oberhettinger, F., Tricomi, F., (1953) Higher Transcendental Functions, 1. , McGraw-Hill, New York
  • Guillera, J., Sondow, J., Double integrals and infinite products for some classical constants via analytic continuations of Lerch's transcendent (2008) Ramanujan J., 16 (3), pp. 247-270. , MR2429900 (2009e:11239)
  • Johnson, B.R., Generalized Lerch zeta function (1974) Pacific J. Math, 53, pp. 189-193. , MR0352020 (50 #4508)
  • Lerch, M., Note sur la fonction (French) (1887) Acta Math, 11 (1-4), pp. 19-24. , MR1554747
  • Navas, L.M., Ruiz, F.J., Varona, J.L., The Möbius inversion formula for Fourier series applied to Bernoulli and Euler polynomials (2011) J. Approx. Theory, 163 (1), pp. 22-40. , MR2741217 (2011j:11032)
  • Navas, L.M., Ruiz, F.J., Varona, J.L., Asymptotic estimates for Apostol- Bernoulli and Apostol-Euler polynomials (2012) Math. Comp, 81 (279), pp. 1707-1722. , MR2904599
  • Navas, L.M., Ruiz, F.J., Varona, J.L., Asymptotic behavior of the Lerch transcendent function (2013) J. Approx. Theory, 170, pp. 21-31. , MR3044042
  • Srivastava, H.M., Choi, J., Series Associated with the Zeta and Related Functions (2001), Kluwer Academic Publishers, Dordrecht. MR1849375 (2003a:11107)Wirtinger, W., Über eine besondere Dirichletsche Reihe (1905) J. Reine Angew. Math, 129, pp. 214-219