Research On Several Problems In Special Function

In this paper,we researched on several problems in special function,pade approximant related to asymptotics for the gamma function and an asymptotic expansions of a ratio of gamma functions,even-order derivative of Jacobi Theta function and modular forms on ?0(2).Based on the Pade approximation method,we develop the approximation formulas of gamma function and Stirling's formula,we present a general result,determine the coefficients.Based on the obtained result,we establish new bounds for the gamma function,we here offer some numerical computations to show the superiority of our sequences are best.We present new approximation formulas and inequalities for Pn,we present more accurate approximations for Pn and determine fixed parameters which pro-vide the best approximations of the form Pn.Based on these approximations,we prove new bounds for Pn.From partial derivative of theta function,we got a class of functions as Fm,we proved that the functions are modular forms on ?0(2)and some identities are established by the functions with weierstrass,?,weber functions,we showed the relations between partial derivative and involution of theta functions,we present some general results and identities.