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The sinc function sinc(x), also called the "sampling function," is a function that arises frequently in signal processing and the theory of Fourier transforms. The full name ...

For a discrete function f(n), the summatory function is defined by F(n)=sum_(k in D)^nf(k), where D is the domain of the function.

Let Gamma(z) be the gamma function and n!! denote a double factorial, then [(Gamma(m+1/2))/(Gamma(m))]^2[1/m+(1/2)^21/(m+1)+((1·3)/(2·4))^21/(m+2)+...]_()_(n) ...

The integral representation of ln[Gamma(z)] by lnGamma(z) = int_1^zpsi_0(z^')dz^' (1) = int_0^infty[(z-1)-(1-e^(-(z-1)t))/(1-e^(-t))](e^(-t))/tdt, (2) where lnGamma(z) is the ...

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; ...

where R[mu+nu-lambda+1]>0, R[lambda]>-1, 0<a<b, J_nu(x) is a Bessel function of the first kind, Gamma(x) is the gamma function, and _2F_1(a,b;c;x) is a hypergeometric ...

The log sine function, also called the logsine function, is defined by S_n=int_0^pi[ln(sinx)]^ndx. (1) The first few cases are given by S_1 = -piln2 (2) S_2 = ...

A function composed of a set of equally spaced jumps of equal length, such as the ceiling function f(x)=[x], floor function f(x)=|_x_|, or nearest integer function f(x)=[x].

A function which has infinitely many derivatives at a point. If a function is not polygenic, it is monogenic.

The identity _2F_1(x,-x;x+n+1;-1)=(Gamma(x+n+1)Gamma(1/2n+1))/(Gamma(x+1/2n+1)Gamma(n+1)), or equivalently ...