# On certain generalized q-Appell polynomial expansions

Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica (2014)

- Volume: 68, Issue: 2
- ISSN: 0365-1029

## Access Full Article

top## Abstract

top## How to cite

topThomas Ernst. "On certain generalized q-Appell polynomial expansions." Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica 68.2 (2014): null. <http://eudml.org/doc/289766>.

@article{ThomasErnst2014,

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 Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica},

language = {eng},

number = {2},

pages = {null},

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

url = {http://eudml.org/doc/289766},

volume = {68},

year = {2014},

}

TY - JOUR

AU - Thomas Ernst

TI - On certain generalized q-Appell polynomial expansions

JO - Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica

PY - 2014

VL - 68

IS - 2

SP - null

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

UR - http://eudml.org/doc/289766

ER -

## References

top- Apostol, T. M., On the Lerch zeta function, Pacific J. Math. 1 (1951), 161–167.
- Dere, R., Simsek, Y., Srivastava, H. M., 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, no. 10 (2013), 3245–3263.
- Ernst, T., A comprehensive treatment of q-calculus, Birkhäuser, Basel, 2012.
- Ernst, T., q-Pascal and q-Wronskian matrices with implications to q-Appell polynomials, J. Discrete Math. 2013.
- Jordan, Ch., Calculus of finite differences, Third Edition, Chelsea Publishing Co., New York, 1950.
- Kim M., Hu S., A note on the Apostol–Bernoulli and Apostol–Euler polynomials, Publ. Math. Debrecen 5587 (2013), 1–16.
- Lee, D. W., On multiple Appell polynomials, Proc. Amer. Math. Soc. 139, no. 6 (2011), 2133–2141.
- Luo, Q.-M., Srivastava, H. M., Some generalizations of the Apostol–Bernoulli and Apostol–Euler polynomials, J. Math. Anal. Appl. 308, no. 1 (2005), 290–302.
- 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.
- Luo, Q.-M., Apostol–Euler polynomials of higher order and Gaussian hypergeometric functions, Taiwanese J. Math. 10, no. 4 (2006), 917–925.
- Milne-Thomson, L. M., The Calculus of Finite Differences, Macmillan and Co., Ltd., London, 1951.
- Nørlund, N. E., Differenzenrechnung, Springer-Verlag, Berlin, 1924.
- 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.
- Sandor, J., Crstici, B., Handbook of number theory II, Kluwer Academic Publishers, Dordrecht, 2004.
- 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.
- Wang, W., Wang, W., Some results on power sums and Apostol-type polynomials, Integral Transforms Spec. Funct. 21, no. 3–4 (2010), 307–318.
- Ward, M., A calculus of sequences, Amer. J. Math. 58 (1936), 255–266.

## Citations in EuDML Documents

top## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.