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1: 10.77 Software
§10.77(ii) Bessel Functions–Real Argument and Integer or Half-Integer Order (including Spherical Bessel Functions)
§10.77(iv) Bessel Functions–Integer or Half-Integer Order and Complex Arguments, including Kelvin Functions
2: 11.4 Basic Properties
§11.4(i) Half-Integer Orders
3: Software Index
4: Bibliography P
  • S. Paszkowski (1991) Evaluation of the Fermi-Dirac integral of half-integer order. Zastos. Mat. 21 (2), pp. 289–301.
  • 5: Bibliography S
  • J. Segura and A. Gil (1998) Parabolic cylinder functions of integer and half-integer orders for nonnegative arguments. Comput. Phys. Comm. 115 (1), pp. 69–86.
  • 6: Bibliography B
  • L. V. Babushkina, M. K. Kerimov, and A. I. Nikitin (1988a) Algorithms for computing Bessel functions of half-integer order with complex arguments. Zh. Vychisl. Mat. i Mat. Fiz. 28 (10), pp. 1449–1460, 1597.
  • 7: 10.21 Zeros
    For further information, including uniform asymptotic expansions, extensions to other branches of the functions and their derivatives, and extensions to half-integer values of the order, see Olver (1954). …
    8: 10.15 Derivatives with Respect to Order
    §10.15 Derivatives with Respect to Order
    Integer Values of ν
    10.15.3 J ν ( z ) ν | ν = n = π 2 Y n ( z ) + n ! 2 ( 1 2 z ) n k = 0 n - 1 ( 1 2 z ) k J k ( z ) k ! ( n - k ) .
    Half-Integer Values of ν
    9: 14.34 Software
  • Adams and Swarztrauber (1997). Integer parameters. Fortran.

  • Braithwaite (1973). Integer parameters. Fortran.

  • Delic (1979a). Integer parameters. Fortran.

  • Gil and Segura (1997). Integer and half-integer parameters. Fortran.

  • Olver and Smith (1983). Integer order. Fortran.

  • 10: 10.38 Derivatives with Respect to Order
    §10.38 Derivatives with Respect to Order
    10.38.2 K ν ( z ) ν = 1 2 π csc ( ν π ) ( I - ν ( z ) ν - I ν ( z ) ν ) - π cot ( ν π ) K ν ( z ) , ν .
    Integer Values of ν
    10.38.4 K ν ( z ) ν | ν = n = n ! 2 ( 1 2 z ) n k = 0 n - 1 ( 1 2 z ) k K k ( z ) k ! ( n - k ) .
    Half-Integer Values of ν