Search Results for "Beta Function"

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. ...

The Glaisher-Kinkelin constant A is defined by lim_(n->infty)(H(n))/(n^(n^2/2+n/2+1/12)e^(-n^2/4))=A (1) (Glaisher 1878, 1894, Voros 1987), where H(n) is the hyperfactorial, ...

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 Dirichlet L-series is a series of the form L_k(s,chi)=sum_(n=1)^inftychi_k(n)n^(-s), (1) where the number theoretic character chi_k(n) is an integer function with period k, ...

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. ...