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A polynomial A_n(x;a) given by the associated Sheffer sequence with f(t)=te^(at), (1) given by A_n(x;a)=x(x-an)^(n-1). (2) The generating function is ...

The duplication formula for Rogers L-function follows from Abel's functional equation and is given by 1/2L(x^2)=L(x)-L(x/(1+x)).

Apéry's numbers are defined by A_n = sum_(k=0)^(n)(n; k)^2(n+k; k)^2 (1) = sum_(k=0)^(n)([(n+k)!]^2)/((k!)^4[(n-k)!]^2) (2) = _4F_3(-n,-n,n+1,n+1;1,1,1;1), (3) where (n; k) ...

The beta function B(p,q) is the name used by Legendre and Whittaker and Watson (1990) for the beta integral (also called the Eulerian integral of the first kind). It is ...

A sequence of polynomials p_n satisfying the identities p_n(x+y)=sum_(k>=0)(n; k)p_k(x)p_(n-k)(y).

A bounded left approximate identity for a normed algebra A is a bounded net {e_alpha}_(alpha in I) with the property lim_(alpha)e_alphaa=a for a in A. Bounded right and ...

There are two identities known as Catalan's identity. The first is F_n^2-F_(n+r)F_(n-r)=(-1)^(n-r)F_r^2, where F_n is a Fibonacci number. Letting r=1 gives Cassini's ...

where _2F_1(a,b;c;z) is a hypergeometric function and _3F_2(a,b,c;d,e;z) is a generalized hypergeometric function.

A notation invented by Dirac which is very useful in quantum mechanics. The notation defines the "ket" vector, denoted |psi>, and its conjugate transpose, called the "bra" ...

A lattice which satisfies the identities (x ^ y) v (x ^ z)=x ^ (y v z) (x v y) ^ (x v z)=x v (y ^ z) is said to be distributive.