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A primitive polynomial is a polynomial that generates all elements of an extension field from a base field. Primitive polynomials are also irreducible polynomials. For any ...

An extended rooted binary tree satisfying the following conditions: 1. Every node has two children, each colored either red or black. 2. Every tree leaf node is colored ...

The asymptotic series for the gamma function is given by (1) (OEIS A001163 and A001164). The coefficient a_n of z^(-n) can given explicitly by ...

While the Catalan numbers are the number of p-good paths from (n,n) to (0,0) which do not cross the diagonal line, the super Catalan numbers count the number of lattice paths ...

A generalization of the p-adic norm first proposed by Kürschák in 1913. A valuation |·| on a field K is a function from K to the real numbers R such that the following ...

The quasiperiodic function defined by d/(dz)lnsigma(z;g_2,g_3)=zeta(z;g_2,g_3), (1) where zeta(z;g_2,g_3) is the Weierstrass zeta function and lim_(z->0)(sigma(z))/z=1. (2) ...

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 ...

The Young tableau (plural, "tableaux") of a Ferrers diagram is obtained by placing the numbers 1, ..., n in the n boxes of the diagram. A "standard" Young tableau is a Young ...

The Zernike polynomials are a set of orthogonal polynomials that arise in the expansion of a wavefront function for optical systems with circular pupils. The odd and even ...

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