The Bessel functions of the first and second kinds studied in Chap. 6 are often referred to as the standard Bessel or cylinder functions. In addition to these, there are a host of related functions also belonging to the general family of cylinder functions, the most notable of which are the modified Bessel functions of the first and second kinds. Although similar in definition to the standard Bessel functions, the modified Bessel functions are most clearly distinguished by their nonoscillatory behavior. For this reason, they often appear in applications that are different in nature from those for the standard functions.
The general family of cylinder functions also include spherical Bessel functions, Hankel functions, Kelvin's functions, Lommel functions, Struve functions, Airy functions, and Anger and Weber functions. Of these, Hankel functions have special significance in that they enable us to obtain asymptotic formulas for large arguments for all the other types of Bessel functions.
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