### 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.

Original language | English |
---|---|

Title of host publication | Lecture Notes in Mathematics |

Publisher | Springer Verlag |

Pages | 1-22 |

Number of pages | 22 |

DOIs | |

Publication status | Published - Jan 1 2010 |

### Publication series

Name | Lecture Notes in Mathematics |
---|---|

Volume | 1994 |

ISSN (Print) | 0075-8434 |

ISSN (Electronic) | 1617-9692 |

### Fingerprint

### Keywords

- Bessel Function
- Gaussian Hypergeometric Function
- Generalize Hypergeometric Function
- Hypergeometric Function
- Spherical Bessel Function

### ASJC Scopus subject areas

- Algebra and Number Theory

### Cite this

*Lecture Notes in Mathematics*(pp. 1-22). (Lecture Notes in Mathematics; Vol. 1994). Springer Verlag. https://doi.org/10.1007/978-3-642-12230-9_1

**Introduction and Preliminary Results.** / Baricz, A.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

*Lecture Notes in Mathematics.*Lecture Notes in Mathematics, vol. 1994, Springer Verlag, pp. 1-22. https://doi.org/10.1007/978-3-642-12230-9_1

}

TY - CHAP

T1 - Introduction and Preliminary Results

AU - Baricz, A.

PY - 2010/1/1

Y1 - 2010/1/1

N2 - 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.

AB - 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.

KW - Bessel Function

KW - Gaussian Hypergeometric Function

KW - Generalize Hypergeometric Function

KW - Hypergeometric Function

KW - Spherical Bessel Function

UR - http://www.scopus.com/inward/record.url?scp=85072857577&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85072857577&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-12230-9_1

DO - 10.1007/978-3-642-12230-9_1

M3 - Chapter

AN - SCOPUS:85072857577

T3 - Lecture Notes in Mathematics

SP - 1

EP - 22

BT - Lecture Notes in Mathematics

PB - Springer Verlag

ER -