## Asymptotic expansions |

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### Contents

INTRODUCTION | 1 |

CHAPTER II | 26 |

SINGULARITIES OF DIFFERENTIAL EQUATIONS | 58 |

Copyright | |

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### Common terms and phrases

Amer analytic functions apply approximations assume asym asymptotic behavior asymptotic expansion asymptotic forms asymptotic power series asymptotic sequence asymptotic series asymptotically equal Bessel functions bounded bounded function calculus chapter Clothbound coefficients complex variable computed by formal constant continuously differentiable convergent Copson derivatives determines discussion elliptic integrals exists extended finite number formal solutions formulas Fourier functions defined fundamental system hence Index infinite series interval introduction irregular singularity Laplace's method linear differential equations linearly independent linearly independent solutions Math mathematical method of steepest neighborhood obtain order relations Paperbound parameters Partial contents partial differential equations path of integration physics possesses an asymptotic power series expansion problems Proc prove ptotic real axis real variable represented asymptotically result satisfies scientific sector stationary points steepest descents steepest paths sufficiently large theorem theory tion twice continuously differentiable uniformly in arg Volterra integral equations zero