no. 10
Analyse harmonique
On the maximum value of a confluent hypergeometric function
Fejzullahu, Bujar Xh.1
1 Departament of Mathematics, University of Prishtina, Mother Teresa 5, 10000 Prishtinë, Kosovo
Comptes Rendus. Mathématique, Tome 359 (2021) no. 10, pp. 1217-1224.

We study the maximum value of the confluent hypergeometric function with oscillatory conditions of parameters. As a consequence, we obtain new inequalities for the Gauss hypergeometric function.

Reçu le :
Accepté le :
Publié le :
DOI : 10.5802/crmath.256
Classification : 33C15, 33C20
Fejzullahu, Bujar Xh. 1

1 Departament of Mathematics, University of Prishtina, Mother Teresa 5, 10000 Prishtinë, Kosovo 
@article{CRMATH_2021__359_10_1217_0,
     author = {Fejzullahu, Bujar Xh.},
     title = {On the maximum value of a confluent hypergeometric function},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1217--1224},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {359},
     number = {10},
     year = {2021},
     doi = {10.5802/crmath.256},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/crmath.256/}
}
TY  - JOUR
AU  - Fejzullahu, Bujar Xh.
TI  - On the maximum value of a confluent hypergeometric function
JO  - Comptes Rendus. Mathématique
PY  - 2021
SP  - 1217
EP  - 1224
VL  - 359
IS  - 10
PB  - Académie des sciences, Paris
UR  - http://www.numdam.org/articles/10.5802/crmath.256/
DO  - 10.5802/crmath.256
LA  - en
ID  - CRMATH_2021__359_10_1217_0
ER  - 
%0 Journal Article
%A Fejzullahu, Bujar Xh.
%T On the maximum value of a confluent hypergeometric function
%J Comptes Rendus. Mathématique
%D 2021
%P 1217-1224
%V 359
%N 10
%I Académie des sciences, Paris
%U http://www.numdam.org/articles/10.5802/crmath.256/
%R 10.5802/crmath.256
%G en
%F CRMATH_2021__359_10_1217_0
Fejzullahu, Bujar Xh. On the maximum value of a confluent hypergeometric function. Comptes Rendus. Mathématique, Tome 359 (2021) no. 10, pp. 1217-1224. doi : 10.5802/crmath.256. http://www.numdam.org/articles/10.5802/crmath.256/

[1] Bailey, Wilfrid N. On the product of two Legendre polynomials with different arguments, Proc. Lond. Math. Soc., Volume 41 (1936), pp. 215-220 | DOI | MR | Zbl

[2] Barnard, Roger W.; Richards, Kendall C.; Tiedeman, Hilari C. A survey of some bounds for Gauss’ hypergeometric function and related bivariate means, J. Math. Inequal., Volume 4 (2010) no. 1, pp. 45-52 | DOI | MR | Zbl

[3] Carlson, Bille C. Some inequalities for hypergeometric functions, Proc. Am. Math. Soc., Volume 17 (1966), pp. 32-39 | DOI | MR

[4] Erber, Thomas Inequalities for hypergeometric functions, Arch. Ration. Mech. Anal., Volume 4 (1960), pp. 341-351 | DOI | MR | Zbl

[5] Glaeske, Hans-Jürgen Die Laguerre-Pinney-Transformation, Aequationes Math., Volume 22 (1981), pp. 73-85 | DOI | MR | Zbl

[6] Karp, D.; Sitnik, Sergei M. Inequalities and monotonicity of ratios for generalized hypergeometric function, J. Approx. Theory, Volume 161 (2009) no. 1, pp. 337-352 | DOI | MR | Zbl

[7] Koornwinder, Tom; Kostenko, Aleksey; Teschl, Gerald Jacobi polynomials, Bernstein-type inequalities and dispersion estimates for the discrete Laguerre operator, Adv. Math., Volume 333 (2018), pp. 796-821 | DOI | MR | Zbl

[8] Krasikov, Ilia An upper bound on Jacobi polynomials, J. Approx. Theory, Volume 149 (2007) no. 2, pp. 116-130 | DOI | MR | Zbl

[9] Krasikov, Ilia; Zarkh, Alexander Equioscillatory property of the Laguerre polynomials, J. Approx. Theory, Volume 162 (2010) no. 11, pp. 2021-2047 | DOI | MR | Zbl

[10] Levin, Eli; Lubinsky, Doron Orthogonal polynomials for exponential weights x 2ρ e -2Q(x) on [0,d). II, J. Approx. Theory, Volume 139 (2006) no. 1-2, pp. 107-143 | DOI | MR | Zbl

[11] Love, Eric R. Inequalities for Laguerre functions, J. Inequal. Appl., Volume 1 (1997) no. 3, pp. 293-299 | MR | Zbl

[12] Luke, Yudell L. The special functions and their approximations, Vol. I, Mathematics in Science and Engineering, 53, Academic Press Inc., 1969 | Zbl

[13] Luke, Yudell L. Inequalities for generalized hypergeometric functions, J. Approx. Theory, Volume 5 (1972), pp. 41-65 | DOI | MR | Zbl

[14] Magnus, Wilhelm; Oberhettinger, Fritz; Soni, Raj Pal Formulas and theorems for the special functions of Mathematical Physics, Grundlehren der Mathematischen Wissenschaften, 52, Springer, 1966 | DOI

[15] Markett, Clemens Product Formulas for Bessel, Whittaker, and Jacobi Functions via the Solution of an Associated Cauchy Problem, Anniversary Volume on Approximation Theory and Functional Analysis (ISNM. International Series of Numerical Mathematics), Volume 65, Birkhäuser, 1984, pp. 449-462 | DOI | MR | Zbl

[16] Markett, Clemens A new proof of Watson’s product formula for Laguerre polynomials via a Cauchy problem associated with a singular differential operator, SIAM J. Math. Anal., Volume 17 (1986), pp. 1010-1032 | DOI | MR | Zbl

[17] Mhaskar, Hrushikesh N.; Saff, Edward B. Where does the sup norm of a weighted polynomial live?(A generalization of incomplete polynomials), Constr. Approx., Volume 1 (1985), pp. 71-91 | DOI | MR | Zbl

[18] NIST Digital Library of Mathematical Functions (Olver, Frank W. J.; Olde Daalhuis, Adri B.; Lozier, Daniel W.; Schneider, Barry I.; Boisvert, Ronald F.; Clark, Charles W.; Miller, Bruce R.; Saunders, Bonita V.; Cohl, Howard S.; McClain, Marjorie A., eds.) (http://dlmf.nist.gov/)

[19] Peetre, Jaak The Weyl transform and Laguerre polynomials, Matematiche, Volume 27 (1973), pp. 301-323 | Zbl

[20] Stempak, Krzysztof A new proof of a Watson’s formula, Can. Math. Bull., Volume 31 (1988) no. 4, pp. 414-418 | DOI | MR | Zbl

[21] Szegö, Gabor Orthogonal polynomials, Colloquium Publications, 23, American Mathematical Society, 1975 | MR

[22] Wang, Fei; Qi, Feng Monotonicity and sharp inequalities related to complete (p,q)-elliptic integrals of the first kind, C. R. Math. Acad. Sci. Paris, Volume 358 (2020) no. 8, pp. 961-970 | DOI | MR | Zbl

[23] Watson, George N. Another note on Laguerre polynomials, J. Lond. Math. Soc., Volume 14 (1939), pp. 19-22 | DOI | MR | Zbl

Cité par Sources :