Dixon-Ferrar Formula
المؤلف:
Gradshteyn, I. S. and Ryzhik, I. M
المصدر:
Eqns. 6.518 and 6.649.1 in Tables of Integrals, Series, and Products, 6th ed. San Diego, CA: Academic Press,
الجزء والصفحة:
...
30-7-2019
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Dixon-Ferrar Formula
Let 
be a Bessel function of the first kind, 
a Bessel function of the second kind, and 
a modified Bessel function of the first kind. Also let ![R[z]>0](http://mathworld.wolfram.com/images/equations/Dixon-FerrarFormula/Inline4.gif)
and ![-1/2<R[nu]<1/2](http://mathworld.wolfram.com/images/equations/Dixon-FerrarFormula/Inline5.gif)
. Then the Dixon-Ferrar formula
(Magnus and Oberhettinger 1948, p. 45; Iyanaga and Kawada 1980, p. 1476; Gradshteyn and Ryzhik 2000, p. 657).
This is a special case of the more general formula
(Magnus and Oberhettinger 1948, p. 44; Gradshteyn and Ryzhik 2000, p. 703) for ![R[z]>1](http://mathworld.wolfram.com/images/equations/Dixon-FerrarFormula/Inline6.gif)
and ![-1<R[nu-mu]<1](http://mathworld.wolfram.com/images/equations/Dixon-FerrarFormula/Inline7.gif)
.
REFERENCES:
Gradshteyn, I. S. and Ryzhik, I. M. Eqns. 6.518 and 6.649.1 in Tables of Integrals, Series, and Products, 6th ed. San Diego, CA: Academic Press, pp. 657 and 703, 2000.
Iyanaga, S. and Kawada, Y. (Eds.). Encyclopedic Dictionary of Mathematics. Cambridge, MA: MIT Press, p. 1476, 1980.
Magnus, W. and Oberhettinger, F. Formeln und Sätze für die speziellen Funktionen der mathematischen Physik, 2nd ed. Berlin: Springer-Verlag, 1948.
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