Is there any closed form for this expression sum_(n=0)^oo ln(n+x)

Mariah Sparks 2022-07-17 Answered
Infinite sum of logarithms
Is there any closed form for this expression
n = 0 ln ( n + x )
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Answers (2)

Dominique Ferrell
Answered 2022-07-18 Author has 18 answers
It's undefined whenever x 0, and the series diverges to infinity whenever x > 0

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Elianna Lawrence
Answered 2022-07-19 Author has 2 answers
Write it as n = 0 k ln ( n + x ) = ln ( n = 0 k ( n + x ) ) = ln ( Γ ( k + x + 1 ) Γ ( x ) ) . If k goes to the expression diverges, if x > 0 or x is not equal to a negative integer.

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