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Advanced Mathematics for Applications by Andrea Prosperetti

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12

The Bessel Equation

 

It would be difficult to overestimate the importance of the Bessel equation and its solutions, the Bessel functions, which arise in a huge variety of problems. Their properties have been studied in minute detail by generations of mathematicians and are recorded in many treatises such as the classic book by Watson (1944). A large collection of formulae and properties can be found especially in Erdélyi et al. (1954), and in Abramowitz & Stegun (1964), Gradshteyn et al. (2007), with many other books carrying at least a selection of the most important relations. Our purpose here is to present a concise framework to illuminate the origin of these relations and their mutual dependencies rather than giving detailed derivations. ...

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