Partition Theoretic Interpretation of Two Identities of Euler

Ananta Kr Bora

doi:10.24297/jam.v19i.8896

Authors

Ananta Kr Bora Concept Jr. College , Assam, India

DOI:

https://doi.org/10.24297/jam.v19i.8896

Keywords:

q-series, Rogers-Ramanujan Identities, Partition, qfactorial

Abstract

In this paper, we have derived a generating function for a restricted partition function. This is in conjunction with two identities of Euler provides a new partition theoretic interpretation of two identities of Euler.

Downloads

Download data is not yet available.

References

L.J. Rogers , “ Second memoir on the expansion of certain infinite products”, Proc. Of London Math.Soc.vol 25 .pp 318 – 343 , 1894

P.A.MacMohan, Combinatory Analysis , Vol2 . Cambridge University Press, New York ,USA , 1916.

B. Gordon, “ A combinatorial generalization of the Rogers – Ramanujan identities ,” Amer.Jour. of Math. Vol . 83 .pp 393-399, 1961.

A.K.Agarwal and M.Goyal , “New Partition Theoritic Interpretations of Rogers – Ramanujan Identities,” International Journal of combinatorics.Vol.2012,Article ID 409505 , Hindawi Publishing Corporation.

B.Gordon ,”Some continued fractions of the Rogers – Ramanujan type,”Duke Mathematical Journal ,Vol32,pp.741-748,1965.

W.G.Connor, “Partition theorems related to some identities of Rogers and Watson,” Transactions of the American Mathematical Society,Vol.214,pp 95-111,1975

M.D.Hirschhorn, “ Some partition theorems of the Rogers-Ramanujan type,”Journal of Combinatorial theory,vol.27,no.1,pp.33-37,1979.

A.K.Agarwal and G.E.Andrews, “Hook differences and lattice paths’” Journal of Statistical Planning and Inference,vol.14,no.1,pp.5-14,1986. [9] m.V.Subbarao and A.K. agarwal, “Further theorems of the Rogers – Ramanujan type theorems,”

Canadian Mathematical Bulletin,vol.31,no.2,pp210-214 , 1988. [10]D.M. Bressoud , “ A new family of partition identities,” Pacific Journal of Mathematics , vol.77,pp.71-74,1978.