Sum to Infinity of Reciprocal of n^4 by 2n Choose n
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Theorem
It is conjectured that:
- $\map \zeta 4 = \ds \dfrac {36} {17} \sum_{n \mathop = 1}^\infty \dfrac 1 {n^4 \dbinom {2 n} n}$
Proof
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Historical Note
On the cited MathWorld page, this result is stated as a truth.
However, according to François Le Lionnais and Jean Brette in their Les Nombres Remarquables of $1983$, this was merely a conjecture.
Sources
- 1983: François Le Lionnais and Jean Brette: Les Nombres Remarquables ... (previous) ... (next): $1,08232 3237 \ldots$
- 1985: D.H. Lehmer: Interesting Series Involving the Central Binomial Coefficient (Amer. Math. Monthly Vol. 92: pp. 449 – 457) www.jstor.org/stable/2322496
- Weisstein, Eric W. "Central Binomial Coefficient." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/CentralBinomialCoefficient.html