About the Project

cross-product

AdvancedHelp

(0.002 seconds)

11—17 of 17 matching pages

11: 10.67 Asymptotic Expansions for Large Argument
§10.67(ii) Cross-Products and Sums of Squares in the Case ν = 0
12: 33.2 Definitions and Basic Properties
§33.2(iv) Wronskians and Cross-Product
13: Bibliography G
  • E. T. Goodwin (1949a) Recurrence relations for cross-products of Bessel functions. Quart. J. Mech. Appl. Math. 2 (1), pp. 72–74.
  • H. P. W. Gottlieb (1985) On the exceptional zeros of cross-products of derivatives of spherical Bessel functions. Z. Angew. Math. Phys. 36 (3), pp. 491–494.
  • 14: Bibliography C
  • J. A. Cochran (1964) Remarks on the zeros of cross-product Bessel functions. J. Soc. Indust. Appl. Math. 12 (3), pp. 580–587.
  • J. A. Cochran (1966a) The analyticity of cross-product Bessel function zeros. Proc. Cambridge Philos. Soc. 62, pp. 215–226.
  • J. A. Cochran (1966b) The asymptotic nature of zeros of cross-product Bessel functions. Quart. J. Mech. Appl. Math. 19 (4), pp. 511–522.
  • 15: 10.21 Zeros
    §10.21(x) Cross-Products
    Higher coefficients in the asymptotic expansions in this subsection can be obtained by expressing the cross-products in terms of the modulus and phase functions (§10.18), and then reverting the asymptotic expansion for the difference of the phase functions. … For information on the zeros of the derivatives of Riccati–Bessel functions, and also on zeros of their cross-products, see Boyer (1969). …
    16: Bibliography M
  • J. Martinek, H. P. Thielman, and E. C. Huebschman (1966) On the zeros of cross-product Bessel functions. J. Math. Mech. 16, pp. 447–452.
  • M. E. Muldoon (1979) On the zeros of a cross-product of Bessel functions of different orders. Z. Angew. Math. Mech. 59 (6), pp. 272–273.
  • 17: Bibliography S
  • L. Z. Salchev and V. B. Popov (1976) A property of the zeros of cross-product Bessel functions of different orders. Z. Angew. Math. Mech. 56 (2), pp. 120–121.