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Basic series corresponding to a class of hypergeometric polynomials†

Published online by Cambridge University Press:  24 October 2008

Jerry L. Fields  and
Jet Wimp
Jerry L. Fields
Affiliation:
Midwest Research Institute, Kansas City, Missouri
Jet Wimp
Affiliation:
Midwest Research Institute, Kansas City, Missouri
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Extract

Let gn(z) be a polynomial of degree n in z. Then there exist constants Πk, nsuch that

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Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 59 , Issue 3 , July 1963 , pp. 599 - 605
Copyright
Copyright © Cambridge Philosophical Society 1963

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References

REFERENCES

(1)Boas, R. P. Jr. and Buck, R. C.Polynomial expansions of analytic functions (Springer-Verlag; Berlin, 1958).CrossRefGoogle Scholar
(2)Erdélyi, A.Magnus, W.Oberhettinger, F. and Tricomi, F. G.Higher transcendental functions, 3 vols. (McGraw-Hill; New York, 1953).Google Scholar
(3)Fields, Jerry L. and Wimp, Jet. Expansions of hypergeometric functions in hypergeometric functions. Math. Tables Aids Comput. 15 (1961), 390–395.CrossRefGoogle Scholar
(4)Erdélyi, A.Magnus, W.Oberhettinger, F. and Tricomi, F. G.Tables of integral transforms, 2 vols. (McGraw-Hill; New York, 1953).Google Scholar
(5)Szegö, G.Orthogonal polynomials (American Mathematical Society Colloquium Publication, 23, revised ed.; New York, 1959).Google Scholar
(6)Lanczos, C. Introduction, National Bureau of Standards Applied Mathematics Series no. 9, Tables of Chebyshev polynomials (U.S. Government Printing Office; Washington D.C., 1952).Google Scholar
(7)Buchholz, H.Die konfluente hypergeometrische funktionen (Springer; Berlin, 1953).CrossRefGoogle Scholar
(8)Watson, G. N.A treatise on the theory of Bessel functions, 2nd ed. (Cambridge, 1945).Google Scholar
(9)Luke, Y. L. and Coleman, R. L.Expansions of hypergeometric functions in series of other hypergeometric functions. Math. Tables Aids Comput. 15 (1961), 235.Google Scholar
(10)Tricomi, F. G.Sulla funzione gamma incompleta. Ann. Mat. Pura Appl. (4), 31 (1950), 263–279.CrossRefGoogle Scholar
(11)Gram, J. P. Note sur le calcul de la fonction ξ(s) de Riemann. Oversigt K. Danske Vidensk. Selskabs Forhandl (1895), 303–308.Google Scholar
(12)Miller, J. C. P. Derivatives of the gamma function; unpublished ms.Google Scholar
(13)National Bureau of Standards. Handbook of mathematical tables, ch. 6. The gamma function and related functions; unpublished ms.Google Scholar
(14)Clenshaw, C. W.A note on the summation of Chebyshev series. Math. Tables Aids Comput. 9 (1955), 118–120.CrossRefGoogle Scholar
(15)Rainville, Earl D.Special functions (Macmillan; New York, 1960).Google Scholar