- #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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- Thread starter mathman
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- #1

mathman

Science Advisor

- 8,022

- 526

- 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##?

- #2

mfb

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For some values there are analytic expressions. It's the Riemann zeta function.

- #3

member 587159

- #4

mathman

Science Advisor

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I should have known! It is the zeta function for all ##c\gt 1##.For some values there are analytic expressions. It's the Riemann zeta function.

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