Title: New series expansions of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:mmultiscripts><mml:mrow><mml:mi>F</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow><mml:none /><mml:mprescripts /><mml:mrow><mml:mn>3</mml:mn></mml:mrow><mml:none /></mml:mmultiscripts></mml:math> function
Abstract: We can use the power series definition of F23(a1,a2,a3;b1,b2;z) to compute this function for z in the unit disk only. In this paper we obtain new expansions of this function that are convergent in larger domains. Some of these expansions involve the polynomial F23(a1,−n,a3;b1,b2;z) evaluated at certain points z. Other expansions involve the Gauss hypergeometric function F12. The domain of convergence is sometimes a disk, other times a half-plane, other times the region |z|2<4|1−z|. The accuracy of the approximation given by these expansions is illustrated with numerical experiments.