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

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

Venting vapor apparatus Patent

Fuel tank pressure-relief device for venting cryogenic liquid vapors through tubes with porous plu

Fused switch

An electric switch device is described which can be used safely even in an explosive environment. The switch has an operating arm, and a moveable actuator which is engaged by the arm and moved between a number of positions in which the arm opens or closes the switch. A fuse is slidably positioned in a passage through the actuator. The fuse can be replaced in the passage by another fuse when the actuator is in one of its many positions. The device is lightweight and compact, is capable of withstanding severe shock, and is not adversely affected by extremes of temperature

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