query: Ramanujan Identity related to JacobiFunction
positive_passages.docid: 154183
positive_passages.text: Proof of a Ramanujan Integral
negative_passages.docid: 145524
negative_passages.text: Proving this identity $\sum_k\frac{1}{k}\binom{2k-2}{k-1}\binom{2n-2k+1}{n-k}=\binom{2n}{n-1}$ using lattice paths
negative_passages.docid: 49938
negative_passages.text: Proof of $a^{\phi (n) +1} \equiv a \pmod{\! n} $ Carmichael generalization of Fermat-Euler's theorem.
negative_passages.docid: 145900
negative_passages.text: Proof of a double summation reduction identity
negative_passages.docid: 83776
negative_passages.text: Is there a direct proof of this lcm identity?
negative_passages.docid: 81753
negative_passages.text: Algorithm for computing Hadamard product of two rational generating functions
negative_passages.docid: 39724
negative_passages.text: Combinatorial Identities
negative_passages.docid: 18518
negative_passages.text: Proof of dilogarithm reflection formula $\zeta(2)-\log(x)\log(1-x)=\operatorname{Li}_2(x)+\operatorname{Li}_2(1-x)$
negative_passages.docid: 60031
negative_passages.text: Showing $\sum\limits_{j=0}^M \frac{M \choose j}{N+M \choose j} = \frac{N+M+1}{N+1}$
negative_passages.docid: 93404
negative_passages.text: J-invariant and isomorphism of elliptic curves over $\mathbb{Q}$
negative_passages.docid: 44575
negative_passages.text: The sigma function (sum of divisors) multiplicative proof
negative_passages.docid: 71564
negative_passages.text: Combinatorial proof of identity involving central binomial coefficients
negative_passages.docid: 26154
negative_passages.text: Motivation for Ramanujan's mysterious $\pi$ formula
negative_passages.docid: 54374
negative_passages.text: Alternating Series Using Other Roots of Unity
negative_passages.docid: 15666
negative_passages.text: explanation for a combinatorial identity involving the binomial coefficient
negative_passages.docid: 46211
negative_passages.text: $(K[x,y,z]/(x^2+y^3+z^7))_{(x,y,z)}$ is a UFD.
negative_passages.docid: 100566
negative_passages.text: Ramanujan's approximation to factorial