## Hypergeometric and Legendre Functions with Applications to Integral Equations of Potential Theory |

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### Contents

Definitions and preliminary formulas | 1 |

Homographlc substitutions of the hypergeometric differential | 9 |

Associated Legendre functions | 33 |

5 other sections not shown

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### Common terms and phrases

absolutely convergent analytic continuation analytic function apply ar)dv circle coefficients condition const converges coordinates corresponding cosh curve cylinder functions defined density differential equation eq VIII Equation VIII equivalent Euler's equation example expressions f-cut finite Fj(V formula function f(r gives half-plane Hence homographic hypergeometric differential equation hypergeometric function identity infinity inside integral equation integral function integral representation integral transform integral VIII interval inversion Landen's transformation lemniscate locus negative integer negative real Neumann series normal derivative normal functions obtained odd function orthogonal parameter path Pj(v plane poles polynomials positive integer positive real Potential given Prom real axis reduced potential region regular singular points replaced satisfies second member simple distribution single-valued singular points sinh strip tanh Toroidal coordinates valid values vanishes variable vhen vhere VIII l(l VTII x-axis z-plane zero