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The Jacobi polynomials, also known as hypergeometric polynomials, occur in the study of rotation groups and in the solution to the equations of motion of the symmetric top. ...

A transformation of a hypergeometric function,

where _8phi_7 is a q-hypergeometric function.

_2phi_1(a,q^(-n);c;q,q)=(a^n(c/a,q)_n)/((a;q)_n), where _2phi_1(a,b;c;q,z) is a q-hypergeometric function.

A Lehmer number is a number generated by a generalization of a Lucas sequence. Let alpha and beta be complex numbers with alpha+beta = sqrt(R) (1) alphabeta = Q, (2) where Q ...

The Prosthaphaeresis formulas, also known as Simpson's formulas, are trigonometry formulas that convert a product of functions into a sum or difference. They are given by ...

A topological groupoid over B is a groupoid G such that B and G are topological spaces and alpha,beta, and multiplication are continuous maps. Here, alpha and beta are maps ...

The wedge product is the product in an exterior algebra. If alpha and beta are differential k-forms of degrees p and q, respectively, then alpha ^ beta=(-1)^(pq)beta ^ alpha. ...

The Werner formulas are the trigonometric product formulas 2sinalphacosbeta = sin(alpha-beta)+sin(alpha+beta) (1) 2cosalphacosbeta = cos(alpha-beta)+cos(alpha+beta) (2) ...

For any real alpha and beta such that beta>alpha, let p(alpha)!=0 and p(beta)!=0 be real polynomials of degree n, and v(x) denote the number of sign changes in the sequence ...