David R. Masson

Calculation of regge poles by continued fractions - I

SummaryWe obtain continued fractions for all the Regge poles of a wide class of potentials. They can be used to calculate the trajectories on an electronic computer. We show graphs of the first Regge trajectory for 20 Yukawa potentials. Our method also gives a new way of calculating binding energies, which are obtained correct to 6 figures in many cases.RiassuntoSi ottengono frazioni continue per tutti i poli di Regge di una vasta categoria di potenziali. Possono essere usate per calcolare le traiettorie con una calculatrice elettronica. Si danno i grafici della prima traiettoria di Regge per 20 potenziali di Yukawa. Questo metodo fornisce un nuovo modo per calcolare le energie di legame, che risultano in molti casi esatte alla sesta cifra.

CONTIGUOUS RELATIONS, CONTINUED FRACTIONS AND ORTHOGONALITY

We examine a special linear combination of balanced very-well-poised

The rotating harmonic oscillator eigenvalue problem. I. Continued fractions and analytic continuation

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Contiguous relations, basic hypergeometric functions, and orthogonal polynomials. III: associated continuous dual q -Hahn polynomials

basic hypergeometric series that is known to satisfy a transformation. We call this

Contiguous relations, basic hypergeometric functions, and orthogonal polynomials. II. Associated big q-Jacobi polynomials☆☆☆

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Associated Wilson polynomials

and show that it satisfies certain three-term contiguous relations. From two sets of contiguous relations for

Difference Equations, Continued Fractions, Jacobi Matrices and Orthogonal Polynomials

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Watson's basic analogue of Ramanujan's Entry 40 and its generalization

we obtain fifty-six pairwise linearly independent solutions to a three-term recurrence that generalizes the recurrence for Askey-Wilson polynomials. The associated continued fraction is evaluated using Pincherles theorem. From this continued fraction we are able to derive a discrete system of biorthogonal rational functions. This ties together Wilsons results for rational biorthogonality, Watsons

Solutions to the associated q -Askey-Wilson polynomial recurrence relation

q

PADE APPROXIMANT AND PARTIAL-WAVE INTEGRAL EQUATION.

-analogue of Ramanujans Entry 40 continued fraction and a conjecture of Askey concerning the latter. Some new