products of Bessel functions
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21: 10.9 Integral Representations
22: Bibliography S
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A property of the zeros of cross-product Bessel functions of different orders.
Z. Angew. Math. Mech. 56 (2), pp. 120–121.
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23: Bibliography G
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Recurrence relations for cross-products of Bessel functions.
Quart. J. Mech. Appl. Math. 2 (1), pp. 72–74.
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On the exceptional zeros of cross-products of derivatives of spherical Bessel functions.
Z. Angew. Math. Phys. 36 (3), pp. 491–494.
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24: 10.22 Integrals
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Products
… ►See also §1.17(ii) for an integral representation of the Dirac delta in terms of a product of Bessel functions. ►Triple Products
… ►Additional infinite integrals over the product of three Bessel functions (including modified Bessel functions) are given in Gervois and Navelet (1984, 1985a, 1985b, 1986a, 1986b). …25: 10.23 Sums
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►For expansions of products of Bessel functions of the first kind in partial fractions see Rogers (2005).
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26: 9.11 Products
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§9.11(iii) Integral Representations
…27: 10.63 Recurrence Relations and Derivatives
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§10.63(i) , , ,
►Let , denote any one of the ordered pairs: … ►§10.63(ii) Cross-Products
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10.63.7
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28: 18.34 Bessel Polynomials
§18.34 Bessel Polynomials
►§18.34(i) Definitions and Recurrence Relation
… ►where is a modified spherical Bessel function (10.49.9), and … ►Hence the full system of polynomials cannot be orthogonal on the line with respect to a positive weight function, but this is possible for a finite system of such polynomials, the Romanovski–Bessel polynomials, if : … ►expressed in terms of Romanovski–Bessel polynomials, Laguerre polynomials or Whittaker functions, we have …29: Bibliography W
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Reduction formulae for products of theta functions.
J. Res. Nat. Inst. Standards and Technology 117, pp. 297–303.
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Rational approximations for the modified Bessel function of the second kind.
Comput. Phys. Comm. 59 (3), pp. 471–493.
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Tables of Summable Series and Integrals Involving Bessel Functions.
Holden-Day, San Francisco, CA.
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Algorithm 44: Bessel functions computed recursively.
Comm. ACM 4 (4), pp. 177–178.
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The asymptotic expansion of the generalized Bessel function.
Proc. London Math. Soc. (2) 38, pp. 257–270.
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