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►In the case of the modifiedBesselfunction
see especially Temme (1975).
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►
…
►For applications of generalized Gauss–Laguerre quadrature (§3.5(v)) to the evaluation of the modifiedBesselfunctions
for and see Gautschi (2002a).
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►
…
►
…
►
…
►Consequently, Besselfunctions
, and modifiedBesselfunctions
, are central to the analysis of microwave and optical transmission in waveguides, including coaxial and fiber.
…
…
►On separation of variables into cylindrical coordinates, the Besselfunctions
, and modifiedBesselfunctions
and , all appear.
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…
►The main functions treated in this chapter are the Besselfunctions
, ; Hankel functions
, ; modifiedBesselfunctions
, ; spherical Besselfunctions
, , , ; modified spherical Besselfunctions
, , ; Kelvin functions
, , , .
For the spherical Besselfunctions and modified spherical Besselfunctions the order is a nonnegative integer.
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►For older notations see British Association for the Advancement of Science (1937, pp. xix–xx) and Watson (1944, Chapters 1–3).