# BSJ Bessel J

## BSJ.1 Introduction |
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Let be a complex variable of and let denote a parameter (independent of ).The function Bessel J (noted ) is defined by the following second order differential equation

BSJ.1.1 |

Although is a singularity of BSJ.1.1, the initial conditions can be given by

BSJ.1.2 |

The formulae of this document are valid for

## BSJ.2 Series and asymptotic expansions |
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## BSJ.2.1 Asymptotic expansion at |
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## BSJ.2.1.2 General form |
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BSJ.2.1.2.1 |

BSJ.2.1.2.2 |

BSJ.2.1.2.3 |

BSJ.2.1.2.4 |

## BSJ.2.2 Asymptotic expansion at |
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## BSJ.2.2.2 General form |
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