## Problems in the Sense of Riemann and Klein |

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### Contents

Linear Differential Equations | 1 |

Ordinary differential equations | 3 |

Linear differential equations with constant coefficients | 12 |

Copyright | |

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### Common terms and phrases

analytic continuation analytic functions angles arbitrary assumes the form Bessel equation boundary values branch points circular arcs closed circuit constant coefficients converge corresponding denote derivative determinant end points equal to zero everywhere existence exponents expressed linearly external finite number Fredholm Fredholm integral equation Fuchsian differential equation Fuchsian singular points fundamental equation fundamental system given Hence hypergeometric differential equation hypergeometric series initial values inside integrand interval left-hand side linear combination linear differential equation linearly independent solutions mapped multiplied number of zeros obtain order pole orthogonal circle particular solutions path of integration Pi(z Pn(z points au a2 polygon polynomial potential prescribed rational coefficients rational functions readily verified real axis region regular at infinity regular power series respect result Riemann Problem right-hand side second order single-valued solubility solution which vanishes solutions of 15.1 substitution theorem transformation unity vanish identically Wronskian x-plane yi(x