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11: 19.20 Special Cases
The general lemniscatic case is … The general lemniscatic case is …
12: 4.2 Definitions
where ph z [ - π , π ] for the principal value of z a , and is unrestricted in the general case. …
13: 15.12 Asymptotic Approximations
For the more general case in which a 2 = o ( c ) and b 2 = o ( c ) see Wagner (1990). …
14: 32.11 Asymptotic Approximations for Real Variables
In the generic case
15: 20.7 Identities
These are specific examples of modular transformations as discussed in §23.15; the corresponding results for the general case are given by Rademacher (1973, pp. 181–183). …
16: Bibliography S
  • F. C. Smith (1939b) Relations among the fundamental solutions of the generalized hypergeometric equation when p = q + 1 . II. Logarithmic cases. Bull. Amer. Math. Soc. 45 (12), pp. 927–935.
  • F. Stenger (1966b) Error bounds for asymptotic solutions of differential equations. II. The general case. J. Res. Nat. Bur. Standards Sect. B 70B, pp. 187–210.
  • 17: 8.21 Generalized Sine and Cosine Integrals
    When ph z = 0 (and when a - 1 , - 3 , - 5 , , in the case of Si ( a , z ) , or a 0 , - 2 , - 4 , , in the case of Ci ( a , z ) ) the principal values of si ( a , z ) , ci ( a , z ) , Si ( a , z ) , and Ci ( a , z ) are defined by (8.21.1) and (8.21.2) with the incomplete gamma functions assuming their principal values (§8.2(i)). …
    18: 25.11 Hurwitz Zeta Function
    For the more general case ζ ( - m , a ) , m = 1 , 2 , , see Elizalde (1986). …
    19: 14.29 Generalizations
    §14.29 Generalizations
    14.29.1 ( 1 - z 2 ) d 2 w d z 2 - 2 z d w d z + ( ν ( ν + 1 ) - μ 1 2 2 ( 1 - z ) - μ 2 2 2 ( 1 + z ) ) w = 0
    are called Generalized Associated Legendre Functions. As in the case of (14.21.1), the solutions are hypergeometric functions, and (14.29.1) reduces to (14.21.1) when μ 1 = μ 2 = μ . … …
    20: 12.14 The Function W ( a , x )
    In other cases the general theory of (12.2.2) is available. …