A NEW RELATION IN Q-POCHHAMMER SYMBOL WITH APPLICATIONS

Authors

  • Aneela Ashraf University of the Punjab
  • Muhammad Khalid Mahmood Punjab University

DOI:

https://doi.org/10.21015/vtcs.v15i3.533

Abstract

In this paper, we propose and investigate a new relation in q-Pochhammer symbol. Further, we establish q-bracket, q-factorial and q-binomial coefficient in term of q-Pochhammer symbol using our proposed relation. As an application,  we express q-Pochhammer symbols in term of ordinary equations to define new surface graphs.

References

Daniel Bump: Automorphic Forms and Representations. Cambridge University Press, UK

G.E. Andrews, The theory of partitions, Addison-Wesley Pub. Co., New York 1976,

Reissued, Cambridge University Press, New York, 1998.

G.E. Andrews and B.C. Berndt, Ramanujan’s Lost Notebook, Part I. Springer, New York

S. Ahlgren and J. Lovejoy, The arithmetic of partitions into distinct parts, Mathematika 48

(2001), 203-211.

D. Penniston, Arithmetic of ‘-regular partition functions, Int. J. Number Theory 4 (2008),

no. 2, 295-302.

N. Calkin, N. Drake, K. James, S. Law, P. Lee, D. Penniston and J. Radder, Divisibility

properties of the 5-regular and 13-regular partition functions, Integers 8 (2008), 2-10.

M.D. Hirschhorn, J.A. Sellers, Elementary proofs of parity results for 5-regular partitions,

Bull. Austral. Math. Soc. 81 (2010) 58-63.

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Published

2019-12-22

Issue

Vol. 7 No. 1 (2019): January-December

Section

Articles

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