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Kelvin defined the Kelvin functions bei and ber according to ber_nu(x)+ibei_nu(x) = J_nu(xe^(3pii/4)) (1) = e^(nupii)J_nu(xe^(-pii/4)), (2) = e^(nupii/2)I_nu(xe^(pii/4)) (3) ...

If any set of points is displaced by X^idx_i where all distance relationships are unchanged (i.e., there is an isometry), then the vector field is called a Killing vector. ...

The simplest interpretation of the Kronecker delta is as the discrete version of the delta function defined by delta_(ij)={0 for i!=j; 1 for i=j. (1) The Kronecker delta is ...

Kummer's first formula is (1) where _2F_1(a,b;c;z) is the hypergeometric function with m!=-1/2, -1, -3/2, ..., and Gamma(z) is the gamma function. The identity can be written ...

The Lebesgue covering dimension is an important dimension and one of the first dimensions investigated. It is defined in terms of covering sets, and is therefore also called ...

The (associated) Legendre function of the first kind P_n^m(z) is the solution to the Legendre differential equation which is regular at the origin. For m,n integers and z ...

A subset E of a topological space S is said to be meager if E is of first category in S, i.e., if E can be written as the countable union of subsets which are nowhere dense ...

1. Find a complete system of invariants, or 2. Decide when two metrics differ only by a coordinate transformation. The most common statement of the problem is, "Given metrics ...

Let f(z) be an analytic function of z, regular in the half-strip S defined by a<x<b and y>0. If f(z) is bounded in S and tends to a limit l as y->infty for a certain fixed ...

The term perimeter refers either to the curve constituting the boundary of a lamina or else to the length of this boundary. The perimeter of a circle is called the ...