الفهرس 
Table of ContentsOnly 14 pages are availabe for public view
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Abstract
The thesis is concerned with the introduction some definition and properties for gamma function and Asymptotic Expansion which is the background for all contents of this thesis. Chapter one: has been devoted to preliminary definitions and some basic properties for gamma function and asymptotic analysis which supply background for the contents of the thesis. Chapter two :gives some 6 Introduction improvements of last results about Ramanujan’s double inequality for n!. Also, it presents simple proofs of some published inequalities of this type which is Hirschorn and villarino’s inequality and a new approximation formula for n!. Chapter three : present new asymptotic formula for factorial n and present new upper bound for gamma function. Chapter four : present new double inequality about Euler constant with the best possible constants through new asymptotic Expansion for Euler constant. Chapter five: present new asymptotic formula for gamma function with recurrence relation for determining some coefficients.