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Let (K,|·|) be a complete non-Archimedean valuated field, with valuation ring R, and let f(X) be a power series with coefficients in R. Suppose at least one of the ...

Let A_r=a_(ij) be a sequence of N symmetric matrices of increasing order with i,j=1, 2, ..., r and r=1, 2, ..., N. Let lambda_k(A_r) be the kth eigenvalue of A_r for k=1, 2, ...

A subgroup is a subset H of group elements of a group G that satisfies the four group requirements. It must therefore contain the identity element. "H is a subgroup of G" is ...

For a linear homogeneous ordinary differential equation, if y_1(x) and y_2(x) are solutions, then so is y_1(x)+y_2(x).

Any linear combination of real spherical harmonics A_lP_l(costheta)+sum_(m=1)^l[A_l^mcos(mphi)+B_l^msin(mphi)]P_l^m(costheta) for l fixed whose sum is not premultiplied by a ...

The numbers of eigenvalues that are positive, negative, or 0 do not change under a congruence transformation. Gradshteyn and Ryzhik (2000) state it as follows: when a ...

The symbol tau (the lower case Greek letter tau) has many common uses in mathematics, as summarized in the following table. 1. tau(n) is an alternate notation for the divisor ...

The topological completion C of a field F with respect to the absolute value |·| is the smallest field containing F for which all Cauchy sequences or rationals converge.

A group of three elements, also called a triad. A triple is therefore a 3-tuple.

A function or transformation f in which f(z) does not overlap z. In modular function theory, a function is called univalent on a subgroup G if it is automorphic under G and ...