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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.
    Weniger, Ernst Joachim 2005. The Spherical Tensor Gradient Operator. Collection of Czechoslovak Chemical Communications, Vol. 70, Issue. 8, p. 1225.
    Weniger, Ernst Joachim 2002. Addition theorems as three-dimensional Taylor expansions. II.B functions and other exponentially decaying functions. International Journal of Quantum Chemistry, Vol. 90, Issue. 1, p. 92.
    Weniger, Ernst Joachim 2000. Addition theorems as three-dimensional Taylor expansions. International Journal of Quantum Chemistry, Vol. 76, Issue. 2, p. 280.
    Prudnikov, A. P. Brychkov, Yu. A. and Marichev, O. I. 1991. Evaluation of integrals and the mellin transform. Journal of Soviet Mathematics, Vol. 54, Issue. 6, p. 1239.
    Weniger, E. Joachim Grotendorst, Johannes and Steinborn, E. Otto 1986. Unified analytical treatment of overlap, two-center nuclear attraction, and Coulomb integrals ofBfunctions via the Fourier-transform method. Physical Review A, Vol. 33, Issue. 6, p. 3688.
    Rashid, M. A. 1986. Simple expressions for radial functions appearing in the expansions of Ym1l1 (∇)F m2l2(r) and ∇2nYm1l1(∇)F m2l2 (r). Journal of Mathematical Physics, Vol. 27, Issue. 2, p. 549.
    Weniger, E. Joachim and Steinborn, E. Otto 1985. A simple derivation of the addition theorems of the irregular solid harmonics, the Helmholtz harmonics, and the modified Helmholtz harmonics. Journal of Mathematical Physics, Vol. 26, Issue. 4, p. 664.
    Weniger, E. Joachim and Steinborn, E. Otto 1983. New representations for the spherical tensor gradient and the spherical delta function. Journal of Mathematical Physics, Vol. 24, Issue. 11, p. 2553.
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Non-classical integrals of Bessel functions

  • S. N. Stuart (a1)
Abstract

Certain definite integrals involving spherical Bessel functions are treated by relating them to Fourier integrals of the point multipoles of potential theory. The main result (apparently new) concerns

where l1, l2 and N are non-negative integers, and r1 and r2 are real; it is interpreted as a generalized function derived by differential operations from the delta function δ(r1 − r2). An ancillary theorem is presented which expresses the gradient ∇2nYlm(∇) of a spherical harmonic function g(r)YLM(Ω) in a form that separates angular and radial variables. A simple means of translating such a function is also derived.

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Copyright
COPYRIGHT: © Australian Mathematical Society 1981
References
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[6]Jette, A. N., “A convenient method for evaluating two centre integrals”, Internal. J. Quantum Chem. 7 (1973), 131–132, 1040.
[7]Jones, D. S., Generalised functions (McGraw-Hill, 1966).
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[10]Miller, W., Lie theory and special functions (Academic Press, 1968).
[11]Milleur, M. B., Twerdochlib, M. and Hirschfelder, J. O., “Bipolar angle averages and two-centre, two-particle integrals involving r 12”, J. Chem. Phys. 45 (1966), 13–20.
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[13]Rowe, E. G. P., “Spherical delta functions and multipole expansions”, J. Math. Phys. 19 (1978), 1962–1968.
[14]Ruedenberg, K., “Bipolare Entwicklungen, Fourier-transformation und molekulare Mehrzentren-Integrale”, Theorel. Chim. Ada 7 (1967), 359–366.
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[19]Stratton, J. A., Electromagnetic theory (McGraw-Hill, 1941).
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