Generalized Twin Prime Formulas

Based on Golomb's arithmetic formulas, Dirichlet series for two classes of twin primes are constructed and related to the roots of the Riemann zeta function in the critical strip.Comment: 17 pages, no figure

Connections between real polynomial solutions of hypergeometric-type differential equations with Rodrigues formula

Starting from the Rodrigues representation of polynomial solutions of the general hypergeometric-type differential equation complementary polynomials are constructed using a natural method. Among the key results is a generating function in closed form leading to short and transparent derivations of recursion relations and an addition theorem. The complementary polynomials satisfy a hypergeometric-type differential equation themselves, have a three-term recursion among others and obey Rodrigues formulas. Applications to the classical polynomials are given.Comment: 13 pages, no figure

Regularities of Twin, Triplet and Multiplet Prime Numbers

Classifications of twin primes are established and then applied to triplets that generalize to all higher multiplets. Mersenne and Fermat twins and triplets are treated in this framework. Regular prime number multiplets are related to quadratic and cubic prime number generating polynomials.Comment: 21 pages; p=21557 in x2+x+p deleted in (vi) of Theor. 4.1 on p.15; to appear in Global J. Pure Applied Math. 8 (2012

Proton Spin Based On Chiral Dynamics

Chiral spin fraction models agree with the proton spin data only when the chiral quark-Goldstone boson couplings are pure spinflip. For axial-vector coupling from soft-pion physics this is true for massless quarks but not for constituent quarks. Axial-vector quark-Goldstone boson couplings with {\bf constituent} quarks are found to be inconsistent with the proton spin data.Comment: 8 pages, Latex, 1 table, no figure

Connections between Romanovski and other polynomials

A connection between Romanovski polynomials and those polynomials that solve the one-dimensional Schr\"odinger equation with the trigonometric Rosen-Morse and hyperbolic Scarf potential is established. The map is constructed by reworking the Rodrigues formula in an elementary and natural way. The generating function is summed in closed form from which recursion relations and addition theorems follow. Relations to some classical polynomials are also given.Comment: 17 pages, no figures, to appear in Central European J. Math. (2007