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.
Highlights
In this paper we have derived generating function for a restricted partition function
Where |q| < 1 and (q; q)n is a rising factorial defined by ∞ 1 − aqi (a; q)n = ∏ 1 − aqn+i n=0
For those whose smallest part is equal to k, we delete k and subtract 2 from all the remaining parts
Summary
In this paper we have derived generating function for a restricted partition function. Where |q| < 1 and (q; q)n is a rising factorial defined by ∞ 1 − aqi (a; q)n = ∏ 1 − aqn+i n=0 In this paper we give the partition theoretic interpretation of the following two identities of Euler : Theorem[1 ]: For a positive integer k , let Ak(n) denote the number of partition of n such that the smallest part (or the only part ) is ≡ k (mod2) and the difference between any two parts is
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