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11: 9.10 Integrals
§9.10(iv) Definite Integrals
12: 4.10 Integrals
Extensive compendia of indefinite and definite integrals of logarithms and exponentials include Apelblat (1983, pp. 16–47), Bierens de Haan (1939), Gröbner and Hofreiter (1949, pp. 107–116), Gröbner and Hofreiter (1950, pp. 52–90), Gradshteyn and Ryzhik (2000, Chapters 2–4), and Prudnikov et al. (1986a, §§1.3, 1.6, 2.3, 2.6).
13: 1.4 Calculus of One Variable
§1.4(v) Definite Integrals
14: Bibliography T
  • I. C. Tang (1969) Some definite integrals and Fourier series for Jacobian elliptic functions. Z. Angew. Math. Mech. 49, pp. 95–96.
  • 15: 25.12 Polylogarithms
    25.12.2 Li 2 ( z ) = - 0 z t - 1 ln ( 1 - t ) d t , z ( 1 , ) .
    25.12.9 n = 1 sin ( n θ ) n 2 = - 0 θ ln ( 2 sin ( 1 2 x ) ) d x .
    16: 33.14 Definitions and Basic Properties
    33.14.15 0 ϕ m , ( r ) ϕ n , ( r ) d r = δ m , n .
    17: Bibliography W
  • R. Wong (1973b) On uniform asymptotic expansion of definite integrals. J. Approximation Theory 7 (1), pp. 76–86.
  • 18: Bibliography G
  • M. L. Glasser (1976) Definite integrals of the complete elliptic integral K . J. Res. Nat. Bur. Standards Sect. B 80B (2), pp. 313–323.
  • 19: 25.11 Hurwitz Zeta Function
    25.11.32 0 a x n ψ ( x ) d x = ( - 1 ) n - 1 ζ ( - n ) + ( - 1 ) n h ( n ) B n + 1 n + 1 - k = 0 n ( - 1 ) k ( n k ) h ( k ) B k + 1 ( a ) k + 1 a n - k + k = 0 n ( - 1 ) k ( n k ) ζ ( - k , a ) a n - k , n = 1 , 2 , , a > 0 ,
    25.11.34 n 0 a ζ ( 1 - n , x ) d x = ζ ( - n , a ) - ζ ( - n ) + B n + 1 - B n + 1 ( a ) n ( n + 1 ) , n = 1 , 2 , , a > 0 .
    20: Errata
  • Equation (33.14.15)


    33.14.15
    0 ϕ m , ( r ) ϕ n , ( r ) d r = δ m , n

    The definite integral, originally written as 0 ϕ n , 2 ( r ) d r = 1 , was clarified and rewritten as an orthogonality relation. This follows from (33.14.14) by combining it with Dunkl (2003, Theorem 2.2).