n-1-H-n-2n-1-pi-2-2H-n-2-8H-2n-2-83-4-4-7log-2-3-8log-2-2-2-2-3-log-4-2-16-Li-4-1-2-where-H-n-m-1-1-2-m-1-n-m-represents-the-nth-gener

Question Number 88004 by M±th+et£s last updated on 07/Apr/20

\underset{n = 1}{\sum^{\infty}} \frac{H_{n}}{2 n + 1} (π^{2} + 2 H_{n}^{(2)} - 8 H_{2 n}^{(2)})

= \frac{83}{4} ζ (4) - 7 l o g (2) ζ (3) - 8 {l o g}^{2} (2) ζ (2) - \frac{2}{3} {l o g}^{4} (2) - 16 {L i}_{4} (\frac{1}{2})

w h e r e H_{n}^{(m)} = 1 + \frac{1}{2^{m}} + \dots . . + \frac{1}{n^{m}} r e p r e s e n t s t h e n t h g e n e r a l i z e d

h a r m o n i c n u m b e r o f o r d e r m, ζ d e n o t e s t h e R i e m a n n

z e t a f u n c t i o n, a n d {L i}_{n} d e s i g n a t e s t h e p o l y l o g a r i t h m

Answered by mind is power last updated on 08/Apr/20

i w i l l T r y

Commented by M±th+et£s last updated on 08/Apr/20

t h a n k y o u s i r