About the Project

Bessel inequality

AdvancedHelp

(0.003 seconds)

1—10 of 27 matching pages

1: 10.37 Inequalities; Monotonicity
§10.37 Inequalities; Monotonicity
2: 10.14 Inequalities; Monotonicity
§10.14 Inequalities; Monotonicity
Kapteyn’s Inequality
For inequalities for the function Γ ( ν + 1 ) ( 2 / x ) ν J ν ( x ) with ν > 1 2 see Neuman (2004). …
3: 18.16 Zeros
Inequalities
Then …
Inequalities
The constant j α , m 2 in (18.16.10) is the best possible since the ratio of the two sides of this inequality tends to 1 as n . … when α ( 1 2 , 1 2 ) . …
4: Bibliography N
  • E. Neuman (2004) Inequalities involving Bessel functions of the first kind. JIPAM. J. Inequal. Pure Appl. Math. 5 (4), pp. Article 94, 4 pp. (electronic).
  • 5: Bibliography L
  • A. Laforgia and M. E. Muldoon (1983) Inequalities and approximations for zeros of Bessel functions of small order. SIAM J. Math. Anal. 14 (2), pp. 383–388.
  • A. Laforgia (1986) Inequalities for Bessel functions. J. Comput. Appl. Math. 15 (1), pp. 75–81.
  • L. Lorch (1993) Some inequalities for the first positive zeros of Bessel functions. SIAM J. Math. Anal. 24 (3), pp. 814–823.
  • 6: 1.8 Fourier Series
    1.8.5 1 π π π | f ( x ) | 2 d x = 1 2 | a 0 | 2 + n = 1 ( | a n | 2 + | b n | 2 ) ,
    1.8.6 1 2 π π π | f ( x ) | 2 d x = n = | c n | 2 ,
    7: Bibliography P
  • R. B. Paris (1984) An inequality for the Bessel function J ν ( ν x ) . SIAM J. Math. Anal. 15 (1), pp. 203–205.
  • 8: Bibliography S
  • J. Segura (2011) Bounds for ratios of modified Bessel functions and associated Turán-type inequalities. J. Math. Anal. Appl. 374 (2), pp. 516–528.
  • K. M. Siegel (1953) An inequality involving Bessel functions of argument nearly equal to their order. Proc. Amer. Math. Soc. 4 (6), pp. 858–859.
  • 9: Bibliography G
  • R. E. Gaunt (2014) Inequalities for modified Bessel functions and their integrals. J. Math. Anal. Appl. 420 (1), pp. 373–386.
  • A. Gervois and H. Navelet (1984) Some integrals involving three Bessel functions when their arguments satisfy the triangle inequalities. J. Math. Phys. 25 (11), pp. 3350–3356.
  • 10: 1.18 Linear Second Order Differential Operators and Eigenfunction Expansions
    For an orthonormal set { v n } in a Hilbert space V Bessel’s inequality holds: …