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Published **2010**
by Springer in Heidelberg, New York .

Written in English

- Hypergeometric functions,
- Inequalities (Mathematics),
- Bessel functions,
- Geometric function theory,
- Bessel-Funktionen

**Edition Notes**

Includes bibliographical references and index.

Statement | Árpád Baricz |

Series | Lecture notes in mathematics -- 1994 |

Classifications | |
---|---|

LC Classifications | QA408 .B275 2010 |

The Physical Object | |

Pagination | xiv, 206 p. : |

Number of Pages | 206 |

ID Numbers | |

Open Library | OL25321429M |

ISBN 10 | 3642122299, 3642122302 |

ISBN 10 | 9783642122293, 9783642122309 |

LC Control Number | 2010926688 |

OCLC/WorldCa | 641540886 |

In this volume we study the generalized Bessel functions of the first kind by using a number of classical and new findings in complex and classical analysis. Our aim is to present interesting geometric properties and functional inequalities for these generalized Bessel functions. Moreover, we extend many known inequalities involving circular and hyperbolic functions to Bessel and modified Bessel functions. In this volume we study the generalized Bessel functions of the first kind by using a number of classical and new findings in complex and classical analysis. Our aim is to present interesting geometric properties and functional inequalities for these generalized Bessel functions. This volume studies the generalized Bessel functions of the first kind by using a number of classical and new findings in complex and classical analysis. It presents interesting geometric properties and functional inequalities for these generalized functions. The purpose of the present paper is to investigate some characterization for generalized Bessel functions of first kind to be in the new subclasses of β uniformly starlike and β uniformly convex functions of order α. Further we point out consequences of our main results.

Bessel Functions a) First Kind: J ν (x) in the solution to Bessel’s equation is referred to as a Bessel function of the ﬁrst Size: KB. 2. Bessel Functions a) First Kind: (x) in the solution to Bessel’s equation is referred to as a Bessel function of the first kind. b) Second Kind: (x) in the solution to Bessel’s equation is referred to as a Bessel function of the second kind or sometimes the Weber function or the Neumann function. BesselJ[n, z] gives the Bessel function of the first kind Jn (z). The purpose of the present paper is to investigate some characterization for generalized Bessel functions of first kind to be in the new subclasses of β uniformly starlike and β uniformly convex.

is known as the Bessel function of the first kind of order ν. The formula is valid providing ν -1, -2, -3,.. Γ(ν) is the gamma function. Numerical calculations of the generalized Bessel of the first kind pdf and cdf vs. Generalized Bessel of the second kind: (a) original pdf and cdf; (b) exponentiated pdf and cdf for í µí»¼ Author: Ilir Progri. Bessel functions, first defined by the mathematician Daniel Bernoulli and then generalized by Friedrich Bessel, are canonical solutions y(x) of Bessel's differential equation + + (−) = for an arbitrary complex number α, the order of the Bessel function. Although α and −α produce the same differential equation, it is conventional to define different Bessel functions for these two values. All four Bessel functions,,, and are defined for all complex values of the parameter and variable, and they are analytical functions of and over the whole complex ‐ and ‐planes.. For fixed, the functions,,, and have an essential singularity the same time, the point is a branch point (except in the case of integer for the two functions).

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