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1: How to Cite
For the gamma function at positive integer argument, see [DLMF, Eq. …
2: 25.6 Integer Arguments
§25.6 Integer Arguments
§25.6(i) Function Values
§25.6(ii) Derivative Values
3: 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
4: 8.28 Software
§8.28(vi) Generalized Exponential Integral for Real Argument and Integer Parameter
5: Software Index
6: 35.2 Laplace Transform
7: 14.34 Software
  • Gil and Segura (1998). Integer parameters and purely imaginary arguments. Fortran.

  • 8: 30.6 Functions of Complex Argument
    30.6.3 𝒲 { Ps n m ( z , γ 2 ) , Qs n m ( z , γ 2 ) } = ( - 1 ) m ( n + m ) ! ( 1 - z 2 ) ( n - m ) ! A n m ( γ 2 ) A n - m ( γ 2 ) ,
    9: 19.5 Maclaurin and Related Expansions
    19.5.4_1 F ( ϕ , k ) = m = 0 ( 1 2 ) m sin 2 m + 1 ϕ ( 2 m + 1 ) m ! F 1 2 ( m + 1 2 , 1 2 m + 3 2 ; sin 2 ϕ ) k 2 m = sin ϕ F 1 ( 1 2 ; 1 2 , 1 2 ; 3 2 ; sin 2 ϕ , k 2 sin 2 ϕ ) ,
    19.5.4_2 E ( ϕ , k ) = m = 0 ( - 1 2 ) m sin 2 m + 1 ϕ ( 2 m + 1 ) m ! F 1 2 ( m + 1 2 , 1 2 m + 3 2 ; sin 2 ϕ ) k 2 m = sin ϕ F 1 ( 1 2 ; 1 2 , - 1 2 ; 3 2 ; sin 2 ϕ , k 2 sin 2 ϕ ) ,
    19.5.4_3 Π ( ϕ , α 2 , k ) = m = 0 ( 1 2 ) m sin 2 m + 1 ϕ ( 2 m + 1 ) m ! F 1 ( m + 1 2 ; 1 2 , 1 ; m + 3 2 ; sin 2 ϕ , α 2 sin 2 ϕ ) k 2 m ,
    10: 20.1 Special Notation
    m , n

    integers.

    z ( )

    the argument.