Inequalities for certain hypergeometric functions

Authors:
C. M. Joshi and J. P. Arya

Journal:
Math. Comp. **38** (1982), 201-205

MSC:
Primary 33A30

DOI:
https://doi.org/10.1090/S0025-5718-1982-0637297-6

MathSciNet review:
637297

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Abstract | References | Similar Articles | Additional Information

Abstract: Theorems on two-sided inequalities for Gauss and Kummer's hypergeometric functions as given by Buschman have been improved. Complex analogues of the said inequalities have been developed and it is pointed out that a similar analysis gives extensions of Luke's, Flett's, and Carlson's theorems.

**[1]**J. L. Brenner, ``A bound for a determinant with dominant main diagonal,''*Proc. Amer. Math. Soc.*, v. 5, 1954, pp. 631-634. MR**0063341 (16:105h)****[2]**J. L. Brenner, ``Bounds for classical polynomials derivable by matrix methods,''*Proc. Amer. Math. Soc.*, v. 30, 1971, pp. 353-362. MR**0280756 (43:6475)****[3]**R. G. Buschman, ``Inequalities for hypergeometric functions,''*Math. Comp.*, v. 30, 1976, pp. 303-305. MR**0390306 (52:11132)****[4]**B. C. Carlson, ``Some inequalities for hypergeometric functions,''*Proc. Amer. Math. Soc.*, v. 17, 1966, pp. 32-39. MR**0188497 (32:5935)****[5]**T. Erber, ``Inequalities for hypergeometric functions,''*Arch. Rational Mech. Anal.*, v. 4, 1959/1960, pp. 341-351. MR**0109899 (22:782)****[6]**A. Erdélyi et al.,*Higher Transcendental Functions*, Vol. I, McGraw-Hill, New York, 1953.**[7]**T. M. Flett, ``Some inequalities for a hypergeometric integral,''*Proc. Edinburgh Math. Soc.*(2), v. 18, 1972, pp. 31-34. MR**0316760 (47:5308)****[8]**Y. L. Luke, ``Inequalities for generalized hypergeometric functions,''*J. Approx. Theory*, v. 5, 1972, pp. 41-65. MR**0350082 (50:2575)****[9]**G. B. Price, ``Bounds for determinants with dominant principal diagonal,''*Proc. Amer. Math. Soc.*, v. 2, 1951, pp. 497-502. MR**0041093 (12:793c)****[10]**H. M. Srivastava & J. L. Brenner, ``Bounds for Jacobi and related polynomials derivable by matrix methods,''*J. Approx. Theory*, v. 12, 1974, pp. 372-377. MR**0374522 (51:10722)**

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1982-0637297-6

Keywords:
Gauss' hypergeometric function,
Kummer's hypergeometric function,
dominant diagonal matrix,
complex parameters and arguments,
inequalities

Article copyright:
© Copyright 1982
American Mathematical Society