Consider the infinite product P ( x , p ) = <munderover> &#x220F;<!-- ∏ -->

June Salas

June Salas

Answered question

2022-06-01

Consider the infinite product
P ( x , p ) = n = 1 ( 1 x n p )
where x 0 and p 0

Answer & Explanation

Ashly Kaufman

Ashly Kaufman

Beginner2022-06-02Added 6 answers

We have the general formula for integer p 2
k = 1 ( 1 z p k p ) = 1 z p k = 0 p 1 1 Γ ( e 2 π i k / p z ) .
Yours is the above evaluated at z = x 1 / p

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