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Preliminary Material on Complex Variables
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applied arbitrary constants Bessel functions Bessel's equation called Chapter choose circle of convergence coefficient Complete the solution complex variable confluent hypergeometric consider corresponding cross-ratio d2w dw defined degree derivative determine dz dz elementary equa equation d2w equation of index equation of Problem equivalent essential singularity example exponents finite plane formula Fuchsian equation Hence holomorphic hypergeometric equation hypergeometric function identity independent variable indicial equation invariant left member linear differential equation linear equation linear fractional transformation mathematician mathematics method multiplication of series neighborhood nomial normal form notation Note ordinary point parameters particular solution polynomial solutions positive integer power series prove recurrence relation region regular singular point result Riccati equation satisfy second order Section solution of equation Solve the equation student substitution Theorem theory tion values Whittaker and Watson Whittaker's equation