A NEW RELATION IN Q-POCHHAMMER SYMBOL WITH APPLICATIONS
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.
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
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.
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License (CC-By) that allows others to share the work with an acknowledgment of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
This work is licensed under a Creative Commons Attribution License CC BY