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Complex Analysis

Multivariable Calculus

A p-adic number is an extension of the field of rationals such that congruences modulo powers of a fixed prime p are related to proximity in the so called "p-adic metric." ...

sum_(y=0)^m(-1)^(m-y)q^((m-y; 2))[m; y]_q(1-wq^m)/(q-wq^y) ×(1-wq^y)^m(-(1-z)/(1-wq^y);q)_y=(1-z)^mq^((m; 2)), where [n; y]_q is a q-binomial coefficient.

The number of representations of n by k squares, allowing zeros and distinguishing signs and order, is denoted r_k(n). The special case k=2 corresponding to two squares is ...

The Andrews-Gordon identity (Andrews 1974) is the analytic counterpart of Gordon's combinatorial generalization of the Rogers-Ramanujan identities (Gordon 1961). It has a ...

In most computer programs and computing environments, the precision of any calculation (even including addition) is limited by the word size of the computer, that is, by ...

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) = ...

Let f(x,y)=u(x,y)+iv(x,y), (1) where z=x+iy, (2) so dz=dx+idy. (3) The total derivative of f with respect to z is then (df)/(dz) = ...