10 Mar
2018
10 Mar
'18
4:24 p.m.
On Sat, Mar 10, 2018 at 5:50 PM, françois mendzina essomba2 via math-fun < math-fun@mailman.xmission.com> wrote:
Hello
In an unfortunate attempt to solve zeta (2n + 1), I became interested in certain functions.
I was able to find:
cos (x / sqrt (2)) * cosh (x / sqrt (2)) = sum ((- 1) ^ n * x ^ (4 * n) / (4 * n)!,n=0..infinity)
but I am lost to the next sum.
sum ((- 1) ^ n * x ^ (3 * n) / (3 * n)!,n=0..infinity) = ???
Do you know the function returned by this sum?
Maple gives: (1/3)*exp(-x)+(2/3)*exp((1/2)*x)*cos((1/2)*3^(1/2)*x)