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The zonal polynomials are a class of orthogonal polynomials. They are a special case of the Jack polynomials corresponding to the case alpha=2.

The partial differential equation ((partial^2)/(partialt^2)-(partial^2)/(partialx^2))((u_(xy))/u)+2(u^2)_(xt)=0.

A generalized hypergeometric function _pF_q[alpha_1,alpha_2,...,alpha_p; beta_1,beta_2,...,beta_q;z], is said to be k-balanced if sum_(i=1)^qbeta_i=k+sum_(i=1)^palpha_i.

A shorthand name for a series with the variable k taken to a negative exponent, e.g., sum_(k=1)^(infty)k^(-p), where p>1. p-series are given in closed form by the Riemann ...

The function defined by [n]_q = [n; 1]_q (1) = (1-q^n)/(1-q) (2) for integer n, where [n; k]_q is a q-binomial coefficient. The q-bracket satisfies lim_(q->1^-)[n]_q=n. (3)

The q-analog of the derivative, defined by (d/(dx))_qf(x)=(f(x)-f(qx))/(x-qx). (1) For example, (d/(dx))_qsinx = (sinx-sin(qx))/(x-qx) (2) (d/(dx))_qlnx = ...

where _8phi_7 is a q-hypergeometric function.

A q-analog of the multinomial coefficient, defined as ([a_1+...+a_n]_q!)/([a_1]_q!...[a_n]_q!), where [n]_q! is a q-factorial.

_8phi_7[a,qa^(1/2),-qa^(1/2),b,c,d,e,q^(-N); a^(1/2),-a^(1/2),(aq)/b,(aq)/c,(aq)/d,(aq)/e,aq^(N+1);q,(aq^(N+2))/(bcde)] ...

If for each positive integer h, the sequence {u_(n+h)-u_n} is uniformly distributed (mod 1), then the sequence {u_n} is uniformly distributed (mod 1) (Montgomery 2001).