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Introduction and Preliminary Results

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1994)

Abstract

We begin with a brief outline of Bessel functions, which will be needed in the next chapters. We recall here the Bessel, modified Bessel, spherical Bessel and modified spherical Bessel functions and define the generalized Bessel function. Some general properties of generalized Bessel functions are discussed in this chapter. These include: recursive formulas, differentiation formula, integral representations. We recall here also the Gaussian hypergeometric function with its basic properties which will have applications in Chap. 3. Finally, at the end of this chapter we list some classical inequalities which will be used in the sequel.

Keywords

  • Bessel Function
  • Hypergeometric Function
  • Generalize Hypergeometric Function
  • Spherical Bessel Function
  • Gaussian Hypergeometric Function

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Correspondence to Árpád Baricz .

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© 2010 Springer-Verlag Berlin Heidelberg

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Baricz, Á. (2010). Introduction and Preliminary Results. In: Generalized Bessel Functions of the First Kind. Lecture Notes in Mathematics(), vol 1994. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12230-9_1

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