Franklin ’ s argument proves an identity of Zagier Robin Chapman

Franklin's Argument Proves an Identity of Zagier

Recently Zagier proved a remarkable q-series identity. We show that this identity can also be proved by modifying Franklin’s classical proof of Euler’s pentagonal number theorem. Mathematics Subject Classification (2000): 05A17 11P81

Combinatorial Proofs of q-Series Identities

We provide combinatorial proofs of six of the ten q-series identities listed in [3, Theorem 3]. Andrews, Jiménez-Urroz and Ono prove these identities using formal manipulation of identities arising in the theory of basic hypergeometric series. Our proofs are purely combinatorial, based on interpreting both sides of the identities as generating functions for certain partitions. One of these iden...

Cosmological argument in proving the existence of God from Imam Khomeini's (RA) point of view

  This article reviews Cosmological argument in proving the existence of God from the viewpoint of Imam Khomeini (RA). At first, various views to the existence of God are reviewed and then its etymology will be reviewed. Cosmological argument proves God through universal premises about truth and world and and the Movement Argument, Casual Argument and Necessity and Possibility Argument are dif...

Partition identities arising from involutions

We give a simple combinatorial proof of three identities of Warnaar. The proofs exploit involutions due to Franklin and Schur.

A New Proof of Some Identities of Bressoud