On a partition identity of Lehmer

Euler's identity equates the number of partitions any non-negative integer n into odd parts and distinct parts. Beck conjectured Andrews proved following companion to identity: excess in all over equals with exactly one even part (possibly repeated). Beck's original conjecture was followed by generalizations so-called “Beck-type” companions other identities. In this paper, we establish a collection Beck-type identities result mentioned Lehmer at 1974 International Congress Mathematicians: an distinct, We also various Lehmer's identity, prove related use both analytic combinatorial methods our proofs.