Problems in the Sense of Riemann and Klein |
Contents
Part | 1 |
The hypergeometric differential equation | 53 |
The solution of the hypergeometric differential equation | 63 |
Copyright | |
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Common terms and phrases
a₁ analytic continuation analytic functions angles arbitrary assumes the form Bessel equation boundary values branch points c₁ closed circuit constant coefficients converge corresponding curve denote derivative determinant end points equal to zero existence exponents factor finite number Fredholm Fuchsian differential equation Fuchsian singular Fuchsian singular points functions y₁(x fundamental equation fundamental system Hence hypergeometric differential equation hypergeometric series initial values inside integral equation integrand interval k₁ left-hand side linear combination linear differential equation linearly independent solutions manner multiplied number of zeros obtain orthogonal circle P₁(z P₂(z parameters particular solutions path of integration points a1 polygon polynomial potential power series readily verified real axis region respect Riemann Problem right-hand side root single-valued singular points solubility solution which vanishes substitution theorem transformation triangle unity variable Wronskian x-plane y₁ Y₂ Ym(x ση