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The exponential function has two different natural q-extensions, denoted e_q(z) and E_q(z). They are defined by e_q(z) = sum_(n=0)^(infty)(z^n)/((q;q)_n) (1) = _1phi_0[0; ...

There are several q-analogs of the sine function. The two natural definitions of the q-sine defined by Koekoek and Swarttouw (1998) are given by sin_q(z) = ...

A q-analog of Zeilberger's algorithm.

A base-b BBP-type formula is a convergent series formula of the type alpha=sum_(k=0)^infty(p(k))/(b^kq(k)) (1) where p(k) and q(k) are integer polynomials in k (Bailey 2000; ...

A special function which is given by the logarithmic derivative of the gamma function (or, depending on the definition, the logarithmic derivative of the factorial). Because ...

The prime zeta function P(s)=sum_(p)1/(p^s), (1) where the sum is taken over primes is a generalization of the Riemann zeta function zeta(s)=sum_(k=1)^infty1/(k^s), (2) where ...

Watson (1939) considered the following three triple integrals, I_1 = 1/(pi^3)int_0^piint_0^piint_0^pi(dudvdw)/(1-cosucosvcosw) (1) = (4[K(1/2sqrt(2))]^2)/(pi^2) (2) = ...

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 ...

The confluent hypergeometric function of the second kind gives the second linearly independent solution to the confluent hypergeometric differential equation. It is also ...

The word "convergent" has a number of different meanings in mathematics. Most commonly, it is an adjective used to describe a convergent sequence or convergent series, where ...