The cylinder function is defined as

(1) |

(2) | |||

(3) |

(4) | |||

(5) |

Then

(6) |

Let , so . Then

(7) |

where is a zeroth order Bessel Function of the First Kind. Let , so , then

(8) |

As defined by Watson (1966), a ``cylinder function'' is any function which satisfies the
Recurrence Relations

(9) |

(10) |

**References**

Watson, G. N. *A Treatise on the Theory of Bessel Functions, 2nd ed.* Cambridge, England: Cambridge University
Press, 1966.

© 1996-9

1999-05-25