second branch cut can be chosen by multiplying with . Application to continued fractions By applying a limiting argument to Gauss's continued fraction it can be shown that and that this continued fraction converges uniformly to a meromorphic function of in every bounded domain that does not include a pole. Notes References External links Confluent Hypergeometric Functions in NIST Digital Library of Mathematical Functions Kummer hypergeometric function on the Wolfram Functions site Tricomi hypergeometric function on the Wolfram Functions site Hypergeometric functions Special hypergeometric functions Special functions