# On certain generalized q-Appell polynomial expansions

Annales UMCS, Mathematica (2015)

- Volume: 68, Issue: 2, page 27-50
- ISSN: 2083-7402

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topThomas Ernst. "On certain generalized q-Appell polynomial expansions." Annales UMCS, Mathematica 68.2 (2015): 27-50. <http://eudml.org/doc/270016>.

@article{ThomasErnst2015,

abstract = {We study q-analogues of three Appell polynomials, the H-polynomials, the Apostol-Bernoulli and Apostol-Euler polynomials, whereby two new q-difference operators and the NOVA q-addition play key roles. The definitions of the new polynomials are by the generating function; like in our book, two forms, NWA and JHC are always given together with tables, symmetry relations and recurrence formulas. It is shown that the complementary argument theorems can be extended to the new polynomials as well as to some related polynomials. In order to find a certain formula, we introduce a q-logarithm. We conclude with a brief discussion of multiple q-Appell polynomials.},

author = {Thomas Ernst},

journal = {Annales UMCS, Mathematica},

keywords = {q-Apostol-Bernoulli polynomials; q-Apostol-Euler polynomials; q-H-polynomials; complementary argument theorem; generating function; multiple q-Appell polynomials; -Apostol-Bernoulli polynomials; -Apostol-Euler polynomials; -H-polynomials; multiple -Appell polynomials},

language = {eng},

number = {2},

pages = {27-50},

title = {On certain generalized q-Appell polynomial expansions},

url = {http://eudml.org/doc/270016},

volume = {68},

year = {2015},

}

TY - JOUR

AU - Thomas Ernst

TI - On certain generalized q-Appell polynomial expansions

JO - Annales UMCS, Mathematica

PY - 2015

VL - 68

IS - 2

SP - 27

EP - 50

AB - We study q-analogues of three Appell polynomials, the H-polynomials, the Apostol-Bernoulli and Apostol-Euler polynomials, whereby two new q-difference operators and the NOVA q-addition play key roles. The definitions of the new polynomials are by the generating function; like in our book, two forms, NWA and JHC are always given together with tables, symmetry relations and recurrence formulas. It is shown that the complementary argument theorems can be extended to the new polynomials as well as to some related polynomials. In order to find a certain formula, we introduce a q-logarithm. We conclude with a brief discussion of multiple q-Appell polynomials.

LA - eng

KW - q-Apostol-Bernoulli polynomials; q-Apostol-Euler polynomials; q-H-polynomials; complementary argument theorem; generating function; multiple q-Appell polynomials; -Apostol-Bernoulli polynomials; -Apostol-Euler polynomials; -H-polynomials; multiple -Appell polynomials

UR - http://eudml.org/doc/270016

ER -

## References

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- [9] Luo, Q.-M., Srivastava, H. M., Some relationships between the Apostol-Bernoulli and Apostol-Euler polynomials, Comput. Math. Appl. 51, no. 3-4 (2006), 631-642. Zbl1099.33011
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- [11] Milne-Thomson, L. M., The Calculus of Finite Differences, Macmillan and Co., Ltd., London, 1951. Zbl59.1111.01
- [12] Nørlund, N. E., Differenzenrechnung, Springer-Verlag, Berlin, 1924.
- [13] Pintér, Á, Srivastava, H. M., Addition theorems for the Appell polynomials and the associated classes of polynomial expansions, Aequationes Math. 85, no. 3 (2013), 483-495.[WoS] Zbl1288.11022
- [14] Sandor, J., Crstici, B., Handbook of number theory II, Kluwer Academic Publishers, Dordrecht, 2004. Zbl1079.11001
- [15] Srivastava, H. M., Özarslan, M. A., Kaanoglu, C., Some generalized Lagrange-based Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi polynomials, Russ. J. Math. Phys. 20, no. 1 (2013), 110-120.[WoS] Zbl1292.11043
- [16] Wang, W., Wang, W., Some results on power sums and Apostol-type polynomials, Integral Transforms Spec. Funct. 21, no. 3-4 (2010), 307-318. Zbl1203.33011
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