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Volumn 233, Issue 11, 2010, Pages 3005-3017

Padé approximation and Apostol-Bernoulli and Apostol-Euler polynomials

Author keywords

Apostol Bernoulli polynomials; Apostol Euler polynomials; Bernoulli numbers; Euler numbers; Pad approximants

Indexed keywords

APOSTOL-BERNOULLI POLYNOMIALS; APPROXIMANTS; BERNOULLI NUMBERS; BERNOULLI POLYNOMIALS; EULER NUMBERS;

EID: 75449101143     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2009.11.050     Document Type: Article
Times cited : (20)

References (30)
  • 1
    • 33645914401 scopus 로고    scopus 로고
    • Recurrences for Bernoulli and Euler polynomials and numbers
    • Agoh T. Recurrences for Bernoulli and Euler polynomials and numbers. Expo. Math. 18 3 (2000) 197-214
    • (2000) Expo. Math. , vol.18 , Issue.3 , pp. 197-214
    • Agoh, T.1
  • 2
    • 67349274435 scopus 로고    scopus 로고
    • Extended Zeilberger's algorithm for identities on Bernoulli and Euler polynomials
    • Chen W.Y.C., and Sun L.H. Extended Zeilberger's algorithm for identities on Bernoulli and Euler polynomials. J. Number Theory 129 9 (2009) 2111-2132
    • (2009) J. Number Theory , vol.129 , Issue.9 , pp. 2111-2132
    • Chen, W.Y.C.1    Sun, L.H.2
  • 3
    • 84972529289 scopus 로고
    • On the Lerch zeta function
    • Apostol T.M. On the Lerch zeta function. Pacific J. Math. 1 (1951) 161-167
    • (1951) Pacific J. Math. , vol.1 , pp. 161-167
    • Apostol, T.M.1
  • 5
    • 19044397438 scopus 로고    scopus 로고
    • On the Apostol-Bernoulli polynomials
    • Luo Q.-M. On the Apostol-Bernoulli polynomials. Cent. Eur. J. Math. 2 4 (2004) 509-515
    • (2004) Cent. Eur. J. Math. , vol.2 , Issue.4 , pp. 509-515
    • Luo, Q.-M.1
  • 6
    • 75449093299 scopus 로고    scopus 로고
    • Apostol-Bernoulli functions, derivative polynomials and Eulerian polynomials
    • Boyadzhiev K.N. Apostol-Bernoulli functions, derivative polynomials and Eulerian polynomials. Adv. Appl. Discrete Math. 1 2 (2008) 109-122
    • (2008) Adv. Appl. Discrete Math. , vol.1 , Issue.2 , pp. 109-122
    • Boyadzhiev, K.N.1
  • 7
    • 19044388957 scopus 로고    scopus 로고
    • Some generalizations of the Apostol-Bernoulli and Apostol-Euler polynomials
    • Luo Q.-M., and Srivastava H.M. Some generalizations of the Apostol-Bernoulli and Apostol-Euler polynomials. J. Math. Anal. Appl. 308 1 (2005) 290-302
    • (2005) J. Math. Anal. Appl. , vol.308 , Issue.1 , pp. 290-302
    • Luo, Q.-M.1    Srivastava, H.M.2
  • 8
    • 33749589040 scopus 로고    scopus 로고
    • Some relationships between the generalized Apostol-Bernoulli polynomials and Hurwitz-Lerch zeta functions
    • Garg M., Jain K., and Srivastava H.M. Some relationships between the generalized Apostol-Bernoulli polynomials and Hurwitz-Lerch zeta functions. Integral Transforms Spec. Funct. 17 11 (2006) 803-815
    • (2006) Integral Transforms Spec. Funct. , vol.17 , Issue.11 , pp. 803-815
    • Garg, M.1    Jain, K.2    Srivastava, H.M.3
  • 9
    • 33747419087 scopus 로고    scopus 로고
    • Apostol-Euler polynomials of higher order and Gaussian hypergeometric functions
    • Luo Q.-M. Apostol-Euler polynomials of higher order and Gaussian hypergeometric functions. Taiwanese J. Math. 10 4 (2006) 917-925
    • (2006) Taiwanese J. Math. , vol.10 , Issue.4 , pp. 917-925
    • Luo, Q.-M.1
  • 10
    • 33745719864 scopus 로고    scopus 로고
    • Some relationships between the Apostol-Bernoulli and Apostol-Euler polynomials
    • Luo Q.-M., and Srivastava H.M. Some relationships between the Apostol-Bernoulli and Apostol-Euler polynomials. Comput. Math. Appl. 51 3-4 (2006) 631-642
    • (2006) Comput. Math. Appl. , vol.51 , Issue.3-4 , pp. 631-642
    • Luo, Q.-M.1    Srivastava, H.M.2
  • 11
    • 68949114125 scopus 로고    scopus 로고
    • The multiplication formulas for the Apostol-Bernoulli and Apostol-Euler polynomials of higher order
    • Luo Q.-M. The multiplication formulas for the Apostol-Bernoulli and Apostol-Euler polynomials of higher order. Integral Transforms Spec. Funct. 20 5-6 (2009) 377-391
    • (2009) Integral Transforms Spec. Funct. , vol.20 , Issue.5-6 , pp. 377-391
    • Luo, Q.-M.1
  • 12
    • 42649116806 scopus 로고    scopus 로고
    • Some q-extensions of the Apostol-Bernoulli and the Apostol-Euler polynomials of order n, and the multiple Hurwitz zeta function
    • Choi J., Anderson P.J., and Srivastava H.M. Some q-extensions of the Apostol-Bernoulli and the Apostol-Euler polynomials of order n, and the multiple Hurwitz zeta function. Appl. Math. Comput. 199 2 (2008) 723-737
    • (2008) Appl. Math. Comput. , vol.199 , Issue.2 , pp. 723-737
    • Choi, J.1    Anderson, P.J.2    Srivastava, H.M.3
  • 13
    • 70349863230 scopus 로고    scopus 로고
    • Fourier expansions and integral representations for the Apostol-Bernoulli and Apostol-Euler polynomials
    • Luo Q.-M. Fourier expansions and integral representations for the Apostol-Bernoulli and Apostol-Euler polynomials. Math. Comp. 78 (2009) 2193-2208
    • (2009) Math. Comp. , vol.78 , pp. 2193-2208
    • Luo, Q.-M.1
  • 15
    • 0034289685 scopus 로고    scopus 로고
    • Convergence acceleration during the 20th century
    • Numerical Analysis 2000, Vol. II: 29 Interpolation and Extrapolation
    • Brezinski C. Convergence acceleration during the 20th century. Numerical Analysis 2000, Vol. II: 29 Interpolation and Extrapolation. J. Comput. Appl. Math. 122 1-2 (2000) 1-21
    • (2000) J. Comput. Appl. Math. , vol.122 , Issue.1-2 , pp. 1-21
    • Brezinski, C.1
  • 16
    • 49349137433 scopus 로고
    • Computation of Padé approximants and continued fractions
    • Brezinski C. Computation of Padé approximants and continued fractions. J. Comput. Appl. Math. 2 2 (1976) 113-123
    • (1976) J. Comput. Appl. Math. , vol.2 , Issue.2 , pp. 113-123
    • Brezinski, C.1
  • 19
    • 0003205429 scopus 로고
    • Padé-type approximation and general orthogonal polynomials
    • Birkhäuser, Verlag, Basel
    • Brezinski C. Padé-type approximation and general orthogonal polynomials. International Series of Numerical Mathematics vol. 50 (1980), Birkhäuser, Verlag, Basel
    • (1980) International Series of Numerical Mathematics , vol.50
    • Brezinski, C.1
  • 20
    • 38249016518 scopus 로고
    • A direct proof of the Christoffel-Darboux identity and its equivalence to the recurrence relationship
    • Extrapolation and Rational Approximation (Luminy, 1989)
    • Brezinski C. A direct proof of the Christoffel-Darboux identity and its equivalence to the recurrence relationship. Extrapolation and Rational Approximation (Luminy, 1989). J. Comput. Appl. Math. 32 1-2 (1990) 17-25
    • (1990) J. Comput. Appl. Math. , vol.32 , Issue.1-2 , pp. 17-25
    • Brezinski, C.1
  • 21
    • 0030102978 scopus 로고    scopus 로고
    • A new proof of the irrationality of ζ (2) and ζ (3) using Padé approximants
    • Prévost M. A new proof of the irrationality of ζ (2) and ζ (3) using Padé approximants. J. Comput. Appl. Math. 67 2 (1996) 219-235
    • (1996) J. Comput. Appl. Math. , vol.67 , Issue.2 , pp. 219-235
    • Prévost, M.1
  • 22
    • 21844505737 scopus 로고
    • A recurrence formula for the Bernoulli numbers
    • Kaneko M. A recurrence formula for the Bernoulli numbers. Proc. Japan Acad. Ser. A Math. Sci. 71 8 (1995) 192-193
    • (1995) Proc. Japan Acad. Ser. A Math. Sci. , vol.71 , Issue.8 , pp. 192-193
    • Kaneko, M.1
  • 23
    • 0142230896 scopus 로고    scopus 로고
    • Applications of the classical umbral calculus
    • (dedicated to the memory of Gian-Carlo Rota)
    • Gessel I.M. Applications of the classical umbral calculus. Algebra Universalis 49 4 (2003) 397-434 (dedicated to the memory of Gian-Carlo Rota)
    • (2003) Algebra Universalis , vol.49 , Issue.4 , pp. 397-434
    • Gessel, I.M.1
  • 24
    • 33645952963 scopus 로고
    • A note on a certain relation among Bernoulli numbers
    • Gel'fand M.B. A note on a certain relation among Bernoulli numbers. Baškir. Gos. Univ. Učen. Zap. Vyp. 31 Ser. Mat. 3 (1968) 215-216
    • (1968) Baškir. Gos. Univ. Učen. Zap. Vyp. , vol.31 , Issue.Ser. Mat. 3 , pp. 215-216
    • Gel'fand, M.B.1
  • 25
    • 0035632422 scopus 로고    scopus 로고
    • A new recurrence formula for Bernoulli numbers
    • Momiyama H. A new recurrence formula for Bernoulli numbers. Fibonacci Quart. 39 3 (2001) 285-288
    • (2001) Fibonacci Quart. , vol.39 , Issue.3 , pp. 285-288
    • Momiyama, H.1
  • 26
    • 13544272847 scopus 로고    scopus 로고
    • Some identities for Bernoulli and Euler polynomials
    • Wu K.-J., Sun Z.-W., and Pan H. Some identities for Bernoulli and Euler polynomials. Fibonacci Quart. 42 4 (2004) 295-299
    • (2004) Fibonacci Quart. , vol.42 , Issue.4 , pp. 295-299
    • Wu, K.-J.1    Sun, Z.-W.2    Pan, H.3
  • 27
    • 75449095124 scopus 로고    scopus 로고
    • Some properties of Bernoulli's numbers, J. Indian Math. Soc. 3 (1911) 219-234
    • AMS Chelsea Publ, Providence, RI
    • Ramanujan S. Some properties of Bernoulli's numbers, J. Indian Math. Soc. 3 (1911) 219-234. Collected Papers of Srinivasa Ramanujan (2000), AMS Chelsea Publ, Providence, RI 1-14
    • (2000) Collected Papers of Srinivasa Ramanujan , pp. 1-14
    • Ramanujan, S.1
  • 28
    • 26844487366 scopus 로고
    • Lacunary recurrence formulas for the numbers of Bernoulli and Euler
    • Lehmer D.H. Lacunary recurrence formulas for the numbers of Bernoulli and Euler. Ann. of Math. (2) 36 3 (1935) 637-649
    • (1935) Ann. of Math. (2) , vol.36 , Issue.3 , pp. 637-649
    • Lehmer, D.H.1
  • 30
    • 40549122974 scopus 로고    scopus 로고
    • Multiple zeta values and application to the lacunary recurrence formulas of Bernoulli's numbers
    • Chen Y.-H. Multiple zeta values and application to the lacunary recurrence formulas of Bernoulli's numbers. J. Phys. Conf. Ser. 96 (2008) 012212
    • (2008) J. Phys. Conf. Ser. , vol.96 , pp. 012212
    • Chen, Y.-H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.