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A zonal harmonic is a spherical harmonic of the form P_l(costheta), i.e., one which reduces to a Legendre polynomial (Whittaker and Watson 1990, p. 302). These harmonics are ...

Let M(X) denote the group of all invertible maps X->X and let G be any group. A homomorphism theta:G->M(X) is called an action of G on X. Therefore, theta satisfies 1. For ...

The conjugate gradient method is not suitable for nonsymmetric systems because the residual vectors cannot be made orthogonal with short recurrences, as proved in Voevodin ...

If (1-z)^(a+b-c)_2F_1(2a,2b;2c;z)=sum_(n=0)^inftya_nz^n, then where (a)_n is a Pochhammer symbol and _2F_1(a,b;c;z) is a hypergeometric function.

A hypergeometric function in which one parameter changes by +1 or -1 is said to be contiguous. There are 26 functions contiguous to _2F_1(a,b;c;x) taking one pair at a time. ...

The first corona of a tile is the set of all tiles that have a common boundary point with that tile (including the original tile itself). The second corona is the set of ...

A functor F is called covariant if it preserves the directions of arrows, i.e., every arrow f:A-->B is mapped to an arrow F(f):F(A)-->F(B).

The cumulative count of property P for a sequence S_n={a_1,a_2,...,a_n} is a sequence of counts of the numbers of elements a_i with i<=k that satisfy P for k=1, 2, ..., n. ...

A cumulative sum is a sequence of partial sums of a given sequence. For example, the cumulative sums of the sequence {a,b,c,...}, are a, a+b, a+b+c, .... Cumulative sums are ...

A function between categories which maps objects to objects and morphisms to morphisms. Functors exist in both covariant and contravariant types.