A convergent series sum

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  • #1
mathman
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Summary:
sum ##\frac{1}{n^c}## where ##c\gt 1##
##\sum_n \frac{1}{n^c}## converges for ##c\gt 1##. Is there an expression for the value of the sum as a function of ##c##?
 

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  • #3
member 587159
No, there is not. A closed expression for ##\sum_{n=1}^\infty \frac{1}{n^3}## is not known. This is Apéry's constant. See https://en.wikipedia.org/wiki/Apéry's_constant for more information.
 
  • #4
mathman
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For some values there are analytic expressions. It's the Riemann zeta function.
I should have known! It is the zeta function for all ##c\gt 1##.
 

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