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generalized exponential integrals

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11: Bibliography O
  • F. W. J. Olver (1991a) Uniform, exponentially improved, asymptotic expansions for the generalized exponential integral. SIAM J. Math. Anal. 22 (5), pp. 1460–1474.
  • F. W. J. Olver (1994b) The Generalized Exponential Integral. In Approximation and Computation (West Lafayette, IN, 1993), R. V. M. Zahar (Ed.), International Series of Numerical Mathematics, Vol. 119, pp. 497–510.
  • 12: 6.4 Analytic Continuation
    The general value of E 1 ( z ) is given by
    6.4.1 E 1 ( z ) = Ein ( z ) - Ln z - γ ;
    13: 8.4 Special Values
    8.4.13 Γ ( 1 - n , z ) = z 1 - n E n ( z ) ,
    14: Bibliography C
  • C. Chiccoli, S. Lorenzutta, and G. Maino (1987) A numerical method for generalized exponential integrals. Comput. Math. Appl. 14 (4), pp. 261–268.
  • C. Chiccoli, S. Lorenzutta, and G. Maino (1988) On the evaluation of generalized exponential integrals E v ( x ) . J. Comput. Phys. 78 (2), pp. 278–287.
  • C. Chiccoli, S. Lorenzutta, and G. Maino (1990b) On a Tricomi series representation for the generalized exponential integral. Internat. J. Comput. Math. 31, pp. 257–262.
  • 15: 13.6 Relations to Other Functions
    When a - b is an integer or a is a positive integer the Kummer functions can be expressed as incomplete gamma functions (or generalized exponential integrals). …
    13.6.6 U ( a , a , z ) = z 1 - a U ( 1 , 2 - a , z ) = z 1 - a e z E a ( z ) = e z Γ ( 1 - a , z ) .
    16: 6.2 Definitions and Interrelations
    The generalized exponential integral E p ( z ) , p , is treated in Chapter 8. …
    17: 13.18 Relations to Other Functions
    When 1 2 - κ ± μ is an integer the Whittaker functions can be expressed as incomplete gamma functions (or generalized exponential integrals). …
    18: 3.10 Continued Fractions
    For special functions see §5.10 (gamma function), §7.9 (error function), §8.9 (incomplete gamma functions), §8.17(v) (incomplete beta function), §8.19(vii) (generalized exponential integral), §§10.10 and 10.33 (quotients of Bessel functions), §13.6 (quotients of confluent hypergeometric functions), §13.19 (quotients of Whittaker functions), and §15.7 (quotients of hypergeometric functions). …
    19: Bibliography
  • 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.
  • 20: Bibliography D
  • T. M. Dunster (1996b) Asymptotics of the generalized exponential integral, and error bounds in the uniform asymptotic smoothing of its Stokes discontinuities. Proc. Roy. Soc. London Ser. A 452, pp. 1351–1367.