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There are (at least) two equations known as Sommerfeld's formula. The first is J_nu(z)=1/(2pi)int_(-eta+iinfty)^(2pi-eta+iinfty)e^(izcost)e^(inu(t-pi/2))dt, where J_nu(z) is ...

The first type of tensor-like object derived from a Riemannian metric g which is used to study the geometry of the metric. Christoffel symbols of the first kind are variously ...

Let the elliptic modulus k satisfy 0<k^2<1, and the Jacobi amplitude be given by phi=amu with -pi/2<phi<pi/2. The incomplete elliptic integral of the first kind is then ...

The ordinary differential equation y^('')+r/zy^'=(Az^m+s/(z^2))y. (1) It has solution y=c_1I_(-nu)((2sqrt(A)z^(m/2+1))/(m+2))z^((1-r)/2) ...

The signed Stirling numbers of the first kind are variously denoted s(n,m) (Riordan 1980, Roman 1984), S_n^((m)) (Fort 1948, Abramowitz and Stegun 1972), S_n^m (Jordan 1950). ...

For R[mu+nu]>0, |argp|<pi/4, and a>0, where J_nu(z) is a Bessel function of the first kind, Gamma(z) is the gamma function, and _1F_1(a;b;z) is a confluent hypergeometric ...

j_n(z)=(z^n)/(2^(n+1)n!)int_0^picos(zcostheta)sin^(2n+1)thetadtheta, where j_n(z) is a spherical Bessel function of the first kind.

Let 0<k^2<1. The incomplete elliptic integral of the third kind is then defined as Pi(n;phi,k) = int_0^phi(dtheta)/((1-nsin^2theta)sqrt(1-k^2sin^2theta)) (1) = ...

The Poisson integral with n=0, J_0(z)=1/piint_0^picos(zcostheta)dtheta, where J_0(z) is a Bessel function of the first kind.

The first solution to Lamé's differential equation, denoted E_n^m(x) for m=1, ..., 2n+1. They are also called Lamé functions. The product of two ellipsoidal harmonics of the ...