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The binomial transform takes the sequence a_0, a_1, a_2, ... to the sequence b_0, b_1, b_2, ... via the transformation b_n=sum_(k=0)^n(-1)^(n-k)(n; k)a_k. The inverse ...

For a power function f(x)=x^k with k>=0 on the interval [0,2L] and periodic with period 2L, the coefficients of the Fourier series are given by a_0 = (2^(k+1)L^k)/(k+1) (1) ...

The Zak transform is a signal transform relevant to time-continuous signals sampled at a uniform rate and an arbitrary clock phase (Janssen 1988). The Zak transform of a ...

An efficient version of the Walsh transform that requires O(nlnn) operations instead of the n^2 required for a direct Walsh transform (Wolfram 2002, p. 1072).

The exponential transform is the transformation of a sequence a_1, a_2, ... into a sequence b_1, b_2, ... according to the equation ...

A piecewise regular function that 1. Has a finite number of finite discontinuities and 2. Has a finite number of extrema can be expanded in a Fourier series which converges ...

The inverse transform sum_(n=1)^infty(a_nx^n)/(n!)=ln(1+sum_(n=1)^infty(b_nx^n)/(n!)) of the exponential transform ...

The isogonal transform of a geometric object is the object obtained by collectively taking the isogonal conjugates of all its points.

The integral transform defined by (Kphi)(x) =int_(-infty)^inftyG_(p+2,q)^(m,n+2)(t|1-nu+ix,1-nu-ix,(a_p); (b_p))phi(t)dt, where G_(c,d)^(a,b) is the Meijer G-function.

A two-sided (doubly infinite) Z-Transform, Z^((2))[{a_n}_(n=-infty)^infty](z)=sum_(n=-infty)^infty(a_n)/(z^n) (Zwillinger 1996; Krantz 1999, p. 214). The bilateral transform ...