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Nicholson's Formula
Let
be aBessel function of the first kind,
aBessel function of the second kind, and
amodified Bessel function of the first kind. Then
 |
for![R[z]>0](/image.pl?url=http%3a%2f%2fmathworld.wolfram.com%2fimages%2fequations%2fNicholsonsFormula%2fInline4.svg&f=jpg&w=240)
, where![R[z]](/image.pl?url=http%3a%2f%2fmathworld.wolfram.com%2fimages%2fequations%2fNicholsonsFormula%2fInline5.svg&f=jpg&w=240)
denotes thereal part of
.
See also
Bessel Function of the First Kind,Bessel Function of the Second Kind,Dixon-Ferrar Formula,Modified Bessel Function of the First Kind,Watson's FormulaExplore with Wolfram|Alpha
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References
Gradshteyn, I. S. and Ryzhik, I. M. Eqn. 6.664.4 inTables of Integrals, Series, and Products, 6th ed. San Diego, CA: Academic Press, p. 707, 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, p. 44, 1948.Referenced on Wolfram|Alpha
Nicholson's FormulaCite this as:
Weisstein, Eric W. "Nicholson's Formula."FromMathWorld--A Wolfram Resource.https://mathworld.wolfram.com/NicholsonsFormula.html