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A sequence s_n(x) is called a Sheffer sequence iff its generating function has the form sum_(k=0)^infty(s_k(x))/(k!)t^k=A(t)e^(xB(t)), (1) where A(t) = A_0+A_1t+A_2t^2+... ...

The Struve function, denoted H_n(z) or occasionally H_n(z), is defined as H_nu(z)=(1/2z)^(nu+1)sum_(k=0)^infty((-1)^k(1/2z)^(2k))/(Gamma(k+3/2)Gamma(k+nu+3/2)), (1) where ...

The Jacobi theta functions are the elliptic analogs of the exponential function, and may be used to express the Jacobi elliptic functions. The theta functions are ...

The important binomial theorem states that sum_(k=0)^n(n; k)r^k=(1+r)^n. (1) Consider sums of powers of binomial coefficients a_n^((r)) = sum_(k=0)^(n)(n; k)^r (2) = ...

The Biggs-Smith graph is cubic symmetric graph F_(102)A on 102 vertices and 153 edges that is also distance-regular with intersection array {3,2,2,2,1,1,1;1,1,1,1,1,1,3} and ...

A cubic symmetric graph is a symmetric cubic (i.e., regular of order 3). Such graphs were first studied by Foster (1932). They have since been the subject of much interest ...

The Desargues graph is the cubic symmetric graph on 20 vertices and 30 edges illustrated above in several embeddings. It is isomorphic to the generalized Petersen graph ...

The detour index omega(G) of a graph G is a graph invariant defined as half the sum of all off-diagonal matrix elements of the detour matrix of G. Unless otherwise stated, ...

The Pappus graph is a cubic symmetric distance-regular graph on 18 vertices, illustrated above in three embeddings. It is Hamiltonian and can be represented in LCF notation ...

The (complete) gamma function Gamma(n) is defined to be an extension of the factorial to complex and real number arguments. It is related to the factorial by Gamma(n)=(n-1)!, ...