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A pair of closed form functions (F,G) is said to be a Wilf-Zeilberger pair if F(n+1,k)-F(n,k)=G(n,k+1)-G(n,k). (1) The Wilf-Zeilberger formalism provides succinct proofs of ...

A q-analog, also called a q-extension or q-generalization, is a mathematical expression parameterized by a quantity q that generalizes a known expression and reduces to the ...

Analytic number theory is the branch of number theory which uses real and complex analysis to investigate various properties of integers and prime numbers. Examples of topics ...

Let P be the set of primes, and let Q_p and Z_p(t) be the fields of p-adic numbers and formal power series over Z_p=(0,1,...,p-1). Further, suppose that D is a "nonprincipal ...

Let the characteristic polynomial of an n×n complex matrix A be written in the form P(lambda) = |lambdaI-A| (1) = ...

A polynomial with 2 terms.

A finite or infinite square matrix with rational entries. (If the matrix is infinite, all but a finite number of entries in each row must be 0.) The sum or product of two ...

Let where (alpha)_j is a Pochhammer symbol, and let alpha be a negative integer. Then S(alpha,beta,m;z)=(Gamma(beta+1-m))/(Gamma(alpha+beta+1-m)), where Gamma(z) is the gamma ...

If, in the Gershgorin circle theorem for a given m, |a_(jj)-a_(mm)|>Lambda_j+Lambda_m for all j!=m, then exactly one eigenvalue of A lies in the disk Gamma_m.

The series producing Brun's constant converges even if there are an infinite number of twin primes, first proved by Brun (1919).