This book is the fruit of my work in the last decade teaching, researching, and solving
problems. This volume offers an unusual collection of problems specializing in three topics …

Some best approximation formulas and inequalities for the Wallis ratio - ScienceDirect Skip
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In this paper, we establish a new asymptotic expansion related to the Wallis ratio. By using
the exponential Bell polynomials, we show that the coefficients of the asymptotic expansion …

Some best approximation formulas and inequalities for the Bateman’s G-function Page 118 Some
best approximation formulas and inequalities for the Bateman’s G-function Ahmed Hegazi1 …

In this paper, the following multiple fractional part integrals I n, β α 1, α 2,⋯, α n=∫[0, 1] n∏
j= 1 nxj α j {S n− 1} β dx 1⋯ dxn and J n, β α=∫[0, 1] n S n α {S n− 1} β dx 1⋯ dxn are studied …

This chapter introduces the reader to a collection of problems that are rarely seen: the
evaluation of exotic integrals involving a fractional part term, called fractional part integrals …

On Ramanujan’s asymptotic formula for n! Page 181 On Ramanujan’s asymptotic formula
for n! Ahmed Hegazi1, Mansour Mahmoud2 and Hend Salah3 Mansoura University, Faculty …