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**Ramanujan's**Dirichlet L-series is defined as f(s)=sum_(n=1)^infty(tau(n))/(n^s), (1) where tau(n) is the tau function. Note that the notation F(s) is sometimes used instead ...

The Jackson-Slater identity is the q-series identity of Rogers-

**Ramanujan**-type given by sum_(k=0)^(infty)(q^(2k^2))/((q)_(2k)) = ...The nth taxicab number Ta(n) is the smallest number representable in n ways as a sum of positive cubes. The numbers derive their name from the Hardy-

**Ramanujan**number Ta(2) = ...An (n,k) fountain is an arrangement of n coins in rows such that exactly k coins are in the bottom row and each coin in the (i+1)st row touches exactly two in the ith row. ...

Let ad=bc, then Hirschhorn's 3-7-5 identity, inspired by the

**Ramanujan**6-10-8 identity, is given by (1) Another version of this identity can be given using linear forms. Let ...Let sigma(n) be the divisor function. Then lim sup_(n->infty)(sigma(n))/(nlnlnn)=e^gamma, where gamma is the Euler-Mascheroni constant.

**Ramanujan**independently discovered a ...The tau conjecture, also known as

**Ramanujan's**hypothesis after its proposer, states that tau(n)∼O(n^(11/2+epsilon)), where tau(n) is the tau function. This was proven by ...A function tau(n) related to the divisor function sigma_k(n), also sometimes called

**Ramanujan's**tau function. It is defined via the Fourier series of the modular discriminant ...Let A_(k,i)(n) denote the number of partitions into n parts not congruent to 0, i, or -i (mod 2k+1). Let B_(k,i)(n) denote the number of partitions of n wherein 1. 1 appears ...

The q-hypergeometric function identity _rphi_s^'[a,qsqrt(a),-qsqrt(a),1/b,1/c,1/d,1/e,1/f; sqrt(a),-sqrt(a),abq,acq,adq,aeq,afq] ...

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