Inequalities for hypergeometric functions
HTML articles powered by AMS MathViewer
- by R. G. Buschman PDF
- Math. Comp. 30 (1976), 303-305 Request permission
Abstract:
The upper and lower bounds for the determinant of a dominant diagonal matrix have been used recently to obtain bounds on the classical orthogonal polynomials. Similar methods are used here on the hypergeometric functions of Gauss and of Kummer.References
- J. L. Brenner, A bound for a determinant with dominant main diagonal, Proc. Amer. Math. Soc. 5 (1954), 631–634. MR 63341, DOI 10.1090/S0002-9939-1954-0063341-8
- T. M. Flett, Some inequalities for a hypergeometric integral, Proc. Edinburgh Math. Soc. (2) 18 (1972/73), 31–34. MR 316760, DOI 10.1017/S0013091500026122 Y. L. LUKE, The Special Functions and Their Approximations. Vol. 1, Math. in Sci. and Engrg., vol. 53, Academic Press, New York, 1969. MR 39 #3039.
- G. Baley Price, Bounds for determinants with dominant principal diagonal, Proc. Amer. Math. Soc. 2 (1951), 497–502. MR 41093, DOI 10.1090/S0002-9939-1951-0041093-2
- D. J. Bordelon and D. K. Ross, Problem 72-l5, “Inequalities for special functions”, SIAM Rev. 15 (1973), 665–670. MR 324085, DOI 10.1137/1015083
- H. M. Srivastava and J. L. Brenner, Bounds for Jacobi and related polynomials derivable by matrix methods, J. Approximation Theory 12 (1974), 372–377. MR 374522, DOI 10.1016/0021-9045(74)90080-x
Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Math. Comp. 30 (1976), 303-305
- MSC: Primary 33A30
- DOI: https://doi.org/10.1090/S0025-5718-1976-0390306-1
- MathSciNet review: 0390306