Uniform bounds for Bessel functions

• Autorzy: Krasikov I.
• Języki publikacji: EN

Abstrakty

EN

For ν > -1/2 and x real we shall establish explicit bounds for the Bessel function Jν(x) which are uniform in x and ν. This work and the recent result of L. J. Landau [7] provide sharp inequalities for all real x.

Słowa kluczowe

EN

Bessel function; bounds

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2006
• Tom: Vol. 12, nr 1
• Strony: 83--91
• Opis fizyczny: Bibliogr. 12 poz.

Twórcy

autor

Krasikov I.

• Department of Mathematical Sciences. Brunel University, Uxbridge UB8 3PH, United Kingdom,

Bibliografia

• [1] Dilcher, K., Stolarsky, K. B., On a class of nonlinear differential operators acting on polynomials, J. Math. Anal. Appl. 170 (1992),382-400.
• [2] Erdelyi, T., Magnus, A. P., Nevai, P., Genemlized Jacobi weights, Christoffel functions, and Jacobi polynomials, SIAM J. Math. Anal. 25 (1994), 602-614.
• [3] Foster, W. H., Krasikov, I., Bounds for the extreme roots of orthogonal polynomials, Int. J. Math. Algorithms 2 (2000), 121-132.
• [4] Foster., W. H., Krasikov, I., Explicit bounds for Hermite polynomials in the oscillatory region, LMS J. Comput. Math. 3 (2000),307-314.
• [5] Jensen, J. L. W. V., Recherches sur la theorie des equations, Acta Math. 36 (1913), 181-195.
• [6] Krasikov, I., Nonnegative quadratic forms and bounds on orthogonal polynomials, J. Approx. Theory 111 (2001), 31-49 .
• [7] Landau, L. J., Bessel functions: monotonicity and bounds, J. London Math. Soc. (2) 61 (2000), 197-215.
• [8] Levin, B. Ja., Distribution of Zeros of Entire Functions, Transl. Math. Monographs 5, Amer. Math. Soc., Providence, RI, 1964, revised ed. 1980.
• [9] Lang, T., Wong, R., "Best possible" upper bounds for the first two positive zeros of the Bessel function Jν (x) : the infinite case, J. Comput. Appl. Math. 71 (1996), 311-329.
• [10] Lorch, L., Uberti, R., "Best possible" upper bounds for the first positive zeros of the Bessel function -the finite case, J. Comput. Appl. Math. 75 (1996),249-258.
• [11] Patrick, M.L., Extension of inequalities of the Laguerre and Thran type, Pacific J. Math. 44 (1973), 675-682.
• [12] Watson, G. N., A Treatise on the Theory of Bessel Functions (2nd ed.), Cambridge Univ. Press, Cambridge, 1995.