log1-1-log3-3-log5-5-log7-7-C-pi-4-2-1-2-log-2pi-1-1-1-3-C-Eulerian-constant-

Question Number 122303 by Dwaipayan Shikari last updated on 15/Nov/20

\frac{l o g 1}{\sqrt{1}} - \frac{l o g 3}{\sqrt{3}} + \frac{l o g 5}{\sqrt{5}} - \frac{l o g 7}{\sqrt{7}} + . . C = (\frac{π}{4} - \frac{γ}{2} - \frac{1}{2} l o g (2 π)) (\frac{1}{\sqrt{1}} - \frac{1}{\sqrt{3}} + . . C)

γ = E u l e r i a n c o n s t a n t

Commented by rs4089 last updated on 15/Nov/20

i t h i n k i t s e x p a n s i o n i s g i v e n b y i n d i a n m a t h e m a t i c i a n s r i n i v a s a r a m a n u j a n t o p r o f e c e r g . h . h a r d y .

Commented by Dwaipayan Shikari last updated on 15/Nov/20

Y e s! B u t i h a v e n o d e r i v a t i o n y e t

Commented by Dwaipayan Shikari last updated on 15/Nov/20

A n y I d e a s i r s ? :)

Answered by mindispower last updated on 15/Nov/20

ζ^{'} (s)

= Σ \frac{- l n (n)}{n^{s}}, s e e e m s s = \frac{1}{2}

w o r c k i n g o n i t