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TIONS IN THE COMPLEX PLANE
RIEMANNPAPPERITZ EQUATION AND THE HYPERGEOMETRIC
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analytic continuation analytic function arbitrary constants asymptotic expansion boundary conditions called Cauchy product change of variable chapter characteristic exponents circle of convergence complex plane complex variable defined determine difference equations equa equal to zero equation 1-6 equation 6-1 equation 8-7 example first-order equation follows from equation formal solutions formula function w(z fundamental set fundamental theorem given by equation Hence homogeneous equation hypergeometric equation hypergeometric function independent variable indicial equation initial conditions integral curve interval isolated singular point linear equation linearly independent linearly independent solutions neighborhood notation obtain ordinary point parameter partial derivatives point of equation pole of order polynomial possess power series recurrence relation region regular singular point regular solution Riemann-Papperitz equation Runge-Kutta method second-order set of solutions simple pole solution curve solution to equation solved substituting equation suppose Taylor series tion values vanish vector Wi(z Wronskian yj+i