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The (unilateral) Z-transform of a sequence {a_k}_(k=0)^infty is defined as Z[{a_k}_(k=0)^infty](z)=sum_(k=0)^infty(a_k)/(z^k). (1) This definition is implemented in the ...

The Bailey mod 9 identities are a set of three Rogers-Ramanujan-like identities appearing as equations (1.6), (1.8), and (1.7) on p. 422 of Bailey (1947) given by A(q) = ...

product_(k=1)^(infty)(1-x^k) = sum_(k=-infty)^(infty)(-1)^kx^(k(3k+1)/2) (1) = 1+sum_(k=1)^(infty)(-1)^k[x^(k(3k-1)/2)+x^(k(3k+1)/2)] (2) = (x)_infty (3) = ...

The Rogers-Selberg identities are a set of three analytic q-series identities of Rogers-Ramanujan-type appearing as equation 33, 32, and 31 in Slater (1952), A(q) = ...

In database structures, two quantities are generally of interest: the average number of comparisons required to 1. Find an existing random record, and 2. Insert a new random ...

Roman (1984, p. 2) describes umbral calculus as the study of the class of Sheffer sequences. Umbral calculus provides a formalism for the systematic derivation and ...

A variable which belongs to exactly one of a finite number of categories.

The converse of Fisher's theorem.

A set of statistical distributions having the same variance.

A polynomial with real positive coefficients and roots which are either negative or pairwise conjugate with negative real parts.