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Not recognizing infinite sum as zeta function?

asked 2024-10-29 11:28:25 +0100

Hi,

Is there a reason why Sage can recognize an infinite series as the zeta function for integers but not fractions (rationals)? For example:

sum(1/t^(2), t, 1, oo), sum(1/t^(3), t, 1, oo), sum(1/t^(11), t, 1, oo)

returns (1/6*pi^2, zeta(3), zeta(11)) But, this:

sum(1/t^(3/2), t, 1, oo), sum(1/t^(5.2), t, 1, oo)

returns just (sum(t^(-3/2), t, 1, +Infinity), sum(t^(-5.2), t, 1, +Infinity))

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answered 2024-10-30 07:44:41 +0100

achrzesz gravatar image

Use:

sum(1/t^(3/2), t, 1, oo,algorithm='sympy'), sum(1/t^QQ(5.2), t, 1, oo,algorithm='sympy')

(zeta(3/2), zeta(26/5))
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Asked: 2024-10-29 11:28:25 +0100

Seen: 48 times

Last updated: Oct 30