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Let P(1/x) be a linear functional acting according to the formula <P(1/x),phi> = Pint(phi(x))/xdx (1) = ...

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 on the reals R is a step function if it can be written as a finite linear combination of semi-open intervals [a,b) subset= R. Therefore, a step function f can be ...

A generalized hypergeometric function _pF_q[alpha_1,alpha_2,...,alpha_p; beta_1,beta_2,...,beta_q;z], is said to be k-balanced if sum_(i=1)^qbeta_i=k+sum_(i=1)^palpha_i.

Lehmer (1938) showed that every positive irrational number x has a unique infinite continued cotangent representation of the form x=cot[sum_(k=0)^infty(-1)^kcot^(-1)b_k], (1) ...

delta(x-t)=sum_(n=0)^inftyphi_n(x)phi_n(t), where delta(x) is the delta function.

The rectangle function Pi(x) is a function that is 0 outside the interval [-1/2,1/2] and unity inside it. It is also called the gate function, pulse function, or window ...

Saalschütz's theorem is the generalized hypergeometric function identity _3F_2[a,b,-n; c,1+a+b-c-n;1]=((c-a)_n(c-b)_n)/((c)_n(c-a-b)_n) (1) which holds for n a nonnegative ...

A quasigroup with an identity element e such that xe=x and ex=x for any x in the quasigroup. All groups are loops. In general, loops are considered to have very little in the ...

If f(x) is piecewise continuous and has a generalized Fourier series sum_(i)a_iphi_i(x) (1) with weighting function w(x), it must be true that ...