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1: 19.7 Connection Formulas
Imaginary-Argument Transformation
2: 10.1 Special Notation
For older notations see British Association for the Advancement of Science (1937, pp. xix–xx) and Watson (1944, Chapters 1–3).
3: Bibliography B
  • L. V. Babushkina, M. K. Kerimov, and A. I. Nikitin (1997) New tables of Bessel functions of complex argument. Comput. Math. Math. Phys. 37 (12), pp. 1480–1482.
  • A. Bañuelos and R. A. Depine (1980) A program for computing the Riemann zeta function for complex argument. Comput. Phys. Comm. 20 (3), pp. 441–445.
  • R. Barakat (1961) Evaluation of the incomplete gamma function of imaginary argument by Chebyshev polynomials. Math. Comp. 15 (73), pp. 7–11.
  • S. Bielski (2013) Orthogonality relations for the associated Legendre functions of imaginary order. Integral Transforms Spec. Funct. 24 (4), pp. 331–337.
  • W. Bühring (1992) Generalized hypergeometric functions at unit argument. Proc. Amer. Math. Soc. 114 (1), pp. 145–153.
  • 4: 8.6 Integral Representations
    8.6.9 Γ ( - a , z e ± π i ) = e z e π i a Γ ( 1 + a ) 0 t a e - z t t - 1 d t , z > 0 , a > - 1 ,
    8.6.10 γ ( a , z ) = 1 2 π i c - i c + i Γ ( s ) a - s z a - s d s , | ph z | < 1 2 π , a 0 , - 1 , - 2 , ,
    8.6.12 Γ ( a , z ) = - z a - 1 e - z Γ ( 1 - a ) 1 2 π i c - i c + i Γ ( s + 1 - a ) π z - s sin ( π s ) d s , | ph z | < 3 2 π , a 1 , 2 , 3 , .