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1: 10.64 Integral Representations
2: 10.38 Derivatives with Respect to Order
§10.38 Derivatives with Respect to Order
3: 10.15 Derivatives with Respect to Order
§10.15 Derivatives with Respect to Order
4: 11.7 Integrals and Sums
§11.7(iv) Integrals with Respect to Order
For integrals of H ν ( x ) and L ν ( x ) with respect to the order ν , see Apelblat (1989). …
5: 11.4 Basic Properties
11.4.27 d d z ( z ν H ν ( z ) ) = z ν H ν - 1 ( z ) ,
11.4.28 d d z ( z - ν H ν ( z ) ) = 2 - ν π Γ ( ν + 3 2 ) - z - ν H ν + 1 ( z ) ,
11.4.31 ν - m ( z ) = z m - ν ( 1 z d d z ) m ( z ν ν ( z ) ) , m = 1 , 2 , 3 , ,
§11.4(vi) Derivatives with Respect to Order
For derivatives with respect to the order ν , see Apelblat (1989) and Brychkov and Geddes (2005). …
6: 14.11 Derivatives with Respect to Degree or Order
§14.11 Derivatives with Respect to Degree or Order
14.11.2 ν Q ν μ ( x ) = - 1 2 π 2 P ν μ ( x ) + π sin ( μ π ) sin ( ν π ) sin ( ( ν + μ ) π ) Q ν μ ( x ) - 1 2 cot ( ( ν + μ ) π ) A ν μ ( x ) + 1 2 csc ( ( ν + μ ) π ) A ν μ ( - x ) ,
7: 10.40 Asymptotic Expansions for Large Argument
ν -Derivative
8: Bibliography F
  • J. L. Fields and Y. L. Luke (1963a) Asymptotic expansions of a class of hypergeometric polynomials with respect to the order. II. J. Math. Anal. Appl. 7 (3), pp. 440–451.
  • J. L. Fields and Y. L. Luke (1963b) Asymptotic expansions of a class of hypergeometric polynomials with respect to the order. J. Math. Anal. Appl. 6 (3), pp. 394–403.
  • J. L. Fields (1965) Asymptotic expansions of a class of hypergeometric polynomials with respect to the order. III. J. Math. Anal. Appl. 12 (3), pp. 593–601.
  • 9: Bibliography
  • A. Apelblat (1989) Derivatives and integrals with respect to the order of the Struve functions H ν ( x ) and L ν ( x ) . J. Math. Anal. Appl. 137 (1), pp. 17–36.
  • A. Apelblat (1991) Integral representation of Kelvin functions and their derivatives with respect to the order. Z. Angew. Math. Phys. 42 (5), pp. 708–714.
  • 10: 10.21 Zeros
    §10.21(xiv) ν -Zeros