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29m
answered Sums of binomial coefficients
5h
comment Prove that $\sum_{k=1}^\infty\frac{1}{16k^4 - 1} = \frac{1}{2} - \frac{\pi}{8}\coth(\frac{\pi}{2})$
There is a relevant technique at this MSE link.
1d
revised How many arrays with crossed cells, order of rows/columns irrelevant
vectors
1d
answered How many arrays with crossed cells, order of rows/columns irrelevant
2d
comment Calculate the binomial sum $ I_n=\sum_{i=0}^n (-1)^i { 2n+1-i \choose i} $
(+1) Very nice work.
2d
revised Calculate the binomial sum $ I_n=\sum_{i=0}^n (-1)^i { 2n+1-i \choose i} $
punctuation
2d
revised Calculate the binomial sum $ I_n=\sum_{i=0}^n (-1)^i { 2n+1-i \choose i} $
simple
Sep
18
comment Calculate the binomial sum $ I_n=\sum_{i=0}^n (-1)^i { 2n+1-i \choose i} $
(+1) Good work. The detour via complex variables appears not to be necessary here.
Sep
18
revised Calculate the binomial sum $ I_n=\sum_{i=0}^n (-1)^i { 2n+1-i \choose i} $
integral
Sep
18
revised Calculate the binomial sum $ I_n=\sum_{i=0}^n (-1)^i { 2n+1-i \choose i} $
period
Sep
18
answered Calculate the binomial sum $ I_n=\sum_{i=0}^n (-1)^i { 2n+1-i \choose i} $
Sep
18
comment Evaluating a series to order “three halves”
The remainder is in the left side of the rectangular contour. (The top and bottom contributions vanish as the height goes to $\pm\infty.$) For more information consult "Mellin Transform Asymptotics" by Sedgewick and Flajolet, INRIA Rapport de Recherche 2956, which explains it better than I ever could.
Sep
17
comment Evaluating a series to order “three halves”
It's an asymptotic.
Sep
16
comment Evaluating a series to order “three halves”
Thanks, and good luck.
Sep
16
comment Combinatorial identity on partitions
There are two proofs by different users at this MSE link.
Sep
16
revised Evaluating a series to order “three halves”
formatting
Sep
16
answered Evaluating a series to order “three halves”
Sep
15
revised How to show this equality
base case
Sep
15
revised How to show this equality
better formatting
Sep
15
answered How to show this equality