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1: 10.75 Tables
  • The main tables in Abramowitz and Stegun (1964, Chapter 9) give J 0 ( x ) to 15D, J 1 ( x ) , J 2 ( x ) , Y 0 ( x ) , Y 1 ( x ) to 10D, Y 2 ( x ) to 8D, x = 0 ( .1 ) 17.5 ; Y n ( x ) ( 2 / π ) J n ( x ) ln x , n = 0 , 1 , x = 0 ( .1 ) 2 , 8D; J n ( x ) , Y n ( x ) , n = 3 ( 1 ) 9 , x = 0 ( .2 ) 20 , 5D or 5S; J n ( x ) , Y n ( x ) , n = 0 ( 1 ) 20 ( 10 ) 50 , 100 , x = 1 , 2 , 5 , 10 , 50 , 100 , 10S; modulus and phase functions x M n ( x ) , θ n ( x ) x , n = 0 , 1 , 2 , 1 / x = 0 ( .01 ) 0.1 , 8D.

  • Abramowitz and Stegun (1964, Chapter 9) tabulates j n , m , J n ( j n , m ) , j n , m , J n ( j n , m ) , n = 0 ( 1 ) 8 , m = 1 ( 1 ) 20 , 5D (10D for n = 0 ), y n , m , Y n ( y n , m ) , y n , m , Y n ( y n , m ) , n = 0 ( 1 ) 8 , m = 1 ( 1 ) 20 , 5D (8D for n = 0 ), J 0 ( j 0 , m x ) , m = 1 ( 1 ) 5 , x = 0 ( .02 ) 1 , 5D. Also included are the first 5 zeros of the functions x J 1 ( x ) λ J 0 ( x ) , J 1 ( x ) λ x J 0 ( x ) , J 0 ( x ) Y 0 ( λ x ) Y 0 ( x ) J 0 ( λ x ) , J 1 ( x ) Y 1 ( λ x ) Y 1 ( x ) J 1 ( λ x ) , J 1 ( x ) Y 0 ( λ x ) Y 1 ( x ) J 0 ( λ x ) for various values of λ and λ 1 in the interval [ 0 , 1 ] , 4–8D.

  • Young and Kirk (1964) tabulates ber n x , bei n x , ker n x , kei n x , n = 0 , 1 , x = 0 ( .1 ) 10 , 15D; ber n x , bei n x , ker n x , kei n x , modulus and phase functions M n ( x ) , θ n ( x ) , N n ( x ) , ϕ n ( x ) , n = 0 , 1 , 2 , x = 0 ( .01 ) 2.5 , 8S, and n = 0 ( 1 ) 10 , x = 0 ( .1 ) 10 , 7S. Also included are auxiliary functions to facilitate interpolation of the tables for n = 0 ( 1 ) 10 for small values of x . (Concerning the phase functions see §10.68(iv).)

  • Zhang and Jin (1996, p. 322) tabulates ber x , ber x , bei x , bei x , ker x , ker x , kei x , kei x , x = 0 ( 1 ) 20 , 7S.

  • Zhang and Jin (1996, p. 323) tabulates the first 20 real zeros of ber x , ber x , bei x , bei x , ker x , ker x , kei x , kei x , 8D.

  • 2: 10.73 Physical Applications
    §10.73(i) Bessel and Modified Bessel Functions
    §10.73(ii) Spherical Bessel Functions
    3: Bibliography
  • M. Abramowitz (1954) Regular and irregular Coulomb wave functions expressed in terms of Bessel-Clifford functions. J. Math. Physics 33, pp. 111–116.
  • Z. Altaç (1996) Integrals involving Bickley and Bessel functions in radiative transfer, and generalized exponential integral functions. J. Heat Transfer 118 (3), pp. 789–792.
  • Y. Ameur and J. Cronvall (2023) Szegő Type Asymptotics for the Reproducing Kernel in Spaces of Full-Plane Weighted Polynomials. Comm. Math. Phys. 398 (3), pp. 1291–1348.
  • D. E. Amos (1974) Computation of modified Bessel functions and their ratios. Math. Comp. 28 (125), pp. 239–251.
  • D. E. Amos (1989) Repeated integrals and derivatives of K Bessel functions. SIAM J. Math. Anal. 20 (1), pp. 169–175.