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Let alpha(x) be a step function with the jump j(x)=(N; x)p^xq^(N-x) (1) at x=0, 1, ..., N, where p>0,q>0, and p+q=1. Then the Krawtchouk polynomial is defined by ...

The Laplace distribution, also called the double exponential distribution, is the distribution of differences between two independent variates with identical exponential ...

The Lucas polynomials are the w-polynomials obtained by setting p(x)=x and q(x)=1 in the Lucas polynomial sequence. It is given explicitly by ...

The Nørlund polynomial (note that the spelling Nörlund also appears in various publications) is a name given by Carlitz (1960) and Adelberg (1997) to the polynomial ...

A number theoretic character, also called a Dirichlet character (because Dirichlet first introduced them in his famous proof that every arithmetic progression with relatively ...

The parabolic cylinder differential equation is the second-order ordinary differential equation y^('')+(nu+1/2-1/4z^2)y=0 (1) whose solution is given by ...

The principal value of an analytic multivalued function is the single value chosen by convention to be returned for a given argument. Complex multivalued functions have ...

A recurrence plot is defined as a plot of the quantity R(t,tau)=H(epsilon-||f(t)-f(tau)||), where H(x) is the Heaviside step function and ||f|| denotes a norm. A recurrence ...

A number n is said to be refactorable, sometimes also called a tau number (Kennedy and Cooper 1990), if it is divisible by the number of its divisors sigma_0(n), where ...

The Riemann-Siegel integral formula is the following representation of the xi-function xi(s) found in Riemann's Nachlass by Bessel-Hagen in 1926 (Siegel 1932; Edwards 2001, ...