## Solved problems: gamma and beta functions, Legendre polynomials, Bessel functions |

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### Contents

Introduction Table and Graph | 1 |

Specific Evaluations of Tx Probs 5911 2223 | 9 |

Infinite Product Expression of rx Prob | 24 |

Copyright | |

29 other sections not shown

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### Common terms and phrases

Accordingly apply Eq approximately arbitrary constants argument becomes infinite Bessel functions Beta function brackets coefficients compute convergent coordinates curve cylinder defined denominator determine differential equation double integral equal established in Prob exponent expression factor find that Eq finite follows Gamma function given by Eq indeterminate form infinite series integral in Eq integrand iterated integral Laplace's equation left in Eq left side Legendre duplication formula Legendre polynomials Legendre's equation Leibniz's Rule limit Maclaurin series multiply namely negative obtained odd function particular solution Pn(x polynomial of degree positive integer powers of h present problem remark replace requires result right in Eq right side Rodrigues's formula satisfies Laplace's equation series in Eq Show side of Eq solution of Eq Stirling's formula summation surface Table V-l temperature distribution term unity vanish variable whence write z-axis