## Asymptotic Analysis, Volume 1 |

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### Contents

Calculation of coefficients | 57 |

The asymptotic behaviour of coefficients of a power series | 75 |

Airy functions | 92 |

Copyright | |

6 other sections not shown

### Common terms and phrases

According analytic function applied assume asymptotic behaviour asymptotic expansion becomes Bessel functions better branch point calculation circle coefficients complex consider constant continuous contour contribution converges corresponding cosh defined derived determined differential difficulty discussion diverges easily equation equivalent Euler Example exists expression fact factorial series formal formula further given gives holds holomorphic hypergeometric function independent infinity integral integral representation interval kind Laplace integral larg z larg z1 leading term lines means method obtain once origin particular phase poles polynomials possible power series Proof properties radius of convergence real axis region relation remainder respect result saddle point sector shows similar simple singularity sinh solution Starting stationary steepest descent line substitution suffices Taylor series term theorem theory tion transformation uniformly valid values variable well-known write written