Inequalities for certain hypergeometric functions
Authors:
C. M. Joshi and J. P. Arya
Journal:
Math. Comp. 38 (1982), 201205
MSC:
Primary 33A30
MathSciNet review:
637297
Fulltext PDF Free Access
Abstract 
References 
Similar Articles 
Additional Information
Abstract: Theorems on twosided 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. 5 (1954),
631–634. MR 0063341
(16,105h), http://dx.doi.org/10.1090/S00029939195400633418
 [2]
J.
L. Brenner, Bounds for classical polynomials
derivable by matrix methods, Proc. Amer. Math.
Soc. 30 (1971),
353–362. MR 0280756
(43 #6475), http://dx.doi.org/10.1090/S00029939197102807563
 [3]
R.
G. Buschman, Inequalities for hypergeometric
functions, Math. Comp. 30
(1976), no. 134, 303–305. MR 0390306
(52 #11132), http://dx.doi.org/10.1090/S00255718197603903061
 [4]
B.
C. Carlson, Some inequalities for hypergeometric
functions, Proc. Amer. Math. Soc. 17 (1966), 32–39. MR 0188497
(32 #5935), http://dx.doi.org/10.1090/S00029939196601884976
 [5]
Thomas
Erber, Inequalities for hypergeometric functions, Arch.
Rational Mech. Anal. 4 (1960), 341–351 (1960). MR 0109899
(22 #782)
 [6]
A. Erdélyi et al., Higher Transcendental Functions, Vol. I, McGrawHill, New York, 1953.
 [7]
T.
M. Flett, Some inequalities for a hypergeometric integral,
Proc. Edinburgh Math. Soc. (2) 18 (1972/73), 31–34.
MR
0316760 (47 #5308)
 [8]
Yudell
L. Luke, Inequalities for generalized hypergeometric
functions, J. Approximation Theory 5 (1972),
41–65. Collection of articles dedicated to J. L. Walsh on his 75th
birthday, I. MR
0350082 (50 #2575)
 [9]
G.
Baley Price, Bounds for determinants with dominant
principal diagonal, Proc. Amer. Math. Soc.
2 (1951),
497–502. MR 0041093
(12,793c), http://dx.doi.org/10.1090/S00029939195100410932
 [10]
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 0374522
(51 #10722)
 [1]
 J. L. Brenner, ``A bound for a determinant with dominant main diagonal,'' Proc. Amer. Math. Soc., v. 5, 1954, pp. 631634. MR 0063341 (16:105h)
 [2]
 J. L. Brenner, ``Bounds for classical polynomials derivable by matrix methods,'' Proc. Amer. Math. Soc., v. 30, 1971, pp. 353362. MR 0280756 (43:6475)
 [3]
 R. G. Buschman, ``Inequalities for hypergeometric functions,'' Math. Comp., v. 30, 1976, pp. 303305. MR 0390306 (52:11132)
 [4]
 B. C. Carlson, ``Some inequalities for hypergeometric functions,'' Proc. Amer. Math. Soc., v. 17, 1966, pp. 3239. MR 0188497 (32:5935)
 [5]
 T. Erber, ``Inequalities for hypergeometric functions,'' Arch. Rational Mech. Anal., v. 4, 1959/1960, pp. 341351. MR 0109899 (22:782)
 [6]
 A. Erdélyi et al., Higher Transcendental Functions, Vol. I, McGrawHill, New York, 1953.
 [7]
 T. M. Flett, ``Some inequalities for a hypergeometric integral,'' Proc. Edinburgh Math. Soc. (2), v. 18, 1972, pp. 3134. MR 0316760 (47:5308)
 [8]
 Y. L. Luke, ``Inequalities for generalized hypergeometric functions,'' J. Approx. Theory, v. 5, 1972, pp. 4165. MR 0350082 (50:2575)
 [9]
 G. B. Price, ``Bounds for determinants with dominant principal diagonal,'' Proc. Amer. Math. Soc., v. 2, 1951, pp. 497502. 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. 372377. MR 0374522 (51:10722)
Similar Articles
Retrieve articles in Mathematics of Computation
with MSC:
33A30
Retrieve articles in all journals
with MSC:
33A30
Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718198206372976
PII:
S 00255718(1982)06372976
Keywords:
Gauss' hypergeometric function,
Kummer's hypergeometric function,
dominant diagonal matrix,
complex parameters and arguments,
inequalities
Article copyright:
© Copyright 1982 American Mathematical Society
