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Legendre and Whittaker and Watson's (1990) term for the beta integral int_0^1x^p(1-x)^qdx, whose solution is the beta function B(p+1,q+1).

Let J_nu(z) be a Bessel function of the first kind, N_nu(z) a Bessel function of the second kind, and j_(nu,n)(z) the zeros of z^(-nu)J_nu(z) in order of ascending real part. ...

The formulas j_n(z) = z^n(-1/zd/(dz))^n(sinz)/z (1) y_n(z) = -z^n(-1/zd/(dz))^n(cosz)/z (2) for n=0, 1, 2, ..., where j_n(z) is a spherical Bessel function of the first kind ...

Polynomials m_k(x;beta,c) which form the Sheffer sequence for g(t) = ((1-c)/(1-ce^t))^beta (1) f(t) = (1-e^t)/(c^(-1)-e^t) (2) and have generating function ...

A sequence of primes q_1<q_2<...<q_k is a Cunningham chain of the first kind (second kind) of length k if q_(i+1)=2q_i+1 (q_(i+1)=2q_i-1) for i=1, ..., k-1. Cunningham primes ...

A generalization of the confluent hypergeometric differential equation given by (1) The solutions are given by y_1 = x^(-A)e^(-f(x))_1F_1(a;b;h(x)) (2) y_2 = ...

Let J_nu(z) be a Bessel function of the first kind, Y_nu(z) a Bessel function of the second kind, and K_nu(z) a modified Bessel function of the first kind. Also let R[z]>0 ...

The Christoffel symbols are tensor-like objects derived from a Riemannian metric g. They are used to study the geometry of the metric and appear, for example, in the geodesic ...

S_n(z) = zj_n(z)=sqrt((piz)/2)J_(n+1/2)(z) (1) C_n(z) = -zn_n(z)=-sqrt((piz)/2)N_(n+1/2)(z), (2) where j_n(z) and n_n(z) are spherical Bessel functions of the first and ...

An integral equation of the form f(x)=int_a^xK(x,t)phi(t)dt, where K(x,t) is the integral kernel, f(x) is a specified function, and phi(t) is the function to be solved for.