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Mat. Zametki, 2012, Volume 91, Issue 1, Pages 54–66 (Mi mz6331)  

This article is cited in 9 scientific papers (total in 9 papers)

Multiplication Formulas for Apostol-Type Polynomials and Multiple Alternating Sums

Qiu-Ming Luo

Department of Mathematics, Chongqing Normal University

Abstract: We investigate multiplication formulas for Apostol-type polynomials and introduce $\lambda$-multiple alternating sums, which are evaluated by Apostol-type polynomials. We derive some explicit recursive formulas and deduce some interesting special cases that involve the classical Raabe formulas and some earlier results of Carlitz and Howard.

Keywords: Apostol-type polynomials, Apostol–Bernoulli numbers and polynomials, Apostol–Euler numbers and polynomials, Apostol–Genocchi numbers and polynomials, multinomial identity, generalized multinomial identity, recursive formula, Raabe's multiplication formula, alternating sum, $\lambda$-multiple alternating sum

DOI: https://doi.org/10.4213/mzm6331

Full text: PDF file (495 kB)
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English version:
Mathematical Notes, 2012, 91:1, 46–57

Bibliographic databases:

UDC: 517
Received: 16.09.2008
Revised: 06.04.2011

Citation: Qiu-Ming Luo, “Multiplication Formulas for Apostol-Type Polynomials and Multiple Alternating Sums”, Mat. Zametki, 91:1 (2012), 54–66; Math. Notes, 91:1 (2012), 46–57

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. R. Dere, Y. Simsek, H. M. Srivastava, “A unified presentation of three families of generalized Apostol type polynomials based upon the theory of the umbral calculus and the umbral algebra”, J. Number Theory, 133:10 (2013), 3245–3263  crossref  mathscinet  zmath  isi  scopus
    2. M.-S. Kim, S. Hu, “A note on the Apostol-Bernoulli and Apostol-Euler polynomials”, Publ. Math.-Debr., 83:3 (2013), 449–464  crossref  mathscinet  zmath  isi  scopus
    3. S. Chen, Y. Cai, Q.-M. Luo, “An extension of generalized Apostol-Euler polynomials”, Adv. Differ. Equ., 2013, 61  crossref  mathscinet  isi  scopus
    4. Yu. He, “A new formula of products of the Apostol–Bernoulli and Apostol–Euler polynomials”, Bull. Malays. Math. Sci. Soc., 39:4 (2016), 1307–1318  crossref  mathscinet  zmath  isi  scopus
    5. V. Kurt, “On the unified family of generalized Apostol-type polynomials of higher order and multiple power sums”, Filomat, 30:4 (2016), 929–935  crossref  mathscinet  zmath  isi  scopus
    6. V. Kurt, “Some symmetry identities for the unified Apostol-type polynomials and multiple power sums”, Filomat, 30:3 (2016), 583–592  crossref  mathscinet  zmath  isi  scopus
    7. B. Kurt, S. Bilgic, “Symmetry identities for the 2-variable unified Apostol-type polynomials”, J. Inequal. Spec. Funct., 8:4 (2017), 96–103  mathscinet  isi
    8. T. Ernst, “Expansion formulas for Apostol type q-Appell polynomials, and their special cases”, Matematiche, 73:1 (2018), 3–24  crossref  isi  scopus
    9. Araci S., Riyasat M., Khan S., Wani Sh.A., “Some Unified Formulas Involving Generalized-Apostol-Type-Gould-Hopper Polynomials and Multiple Power Sums”, J. Math. Comput. Sci.-JMCS, 19:2 (2019), 97–115  crossref  isi
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