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Results tagged with nt.number-theory
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user 3648
Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions
5
votes
Help with a double sum, please
Some observations.
Define
$$T(N)=\binom{2N}{N}\sum_{j=0}^{N-1}\left[\binom{2(N-j)}{N-j} \cdot (N-j) \cdot 2^{(N+j+1)}\right]^{-1}.$$
Then
$$S(m)=\sum_{k=0}^m (-1)^k \binom{m}{k} T(m+k) .$$
Experimen …
