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Improving Stirling's formula
Get PDFWe calculated the optimal values of the real parameters and in such a way that the asymptotic formula
gives the best accurate values for . Our estimations improve the classical Stirling and Burnside's formulas and their several recent improvements due to the author and C. Mortici. Apart from their simplicities and beauties our formulas give very accurate values for factorial . Also, our results lead to new upper and lower bounds for the gamma function and recover some published inequalities for the gamma function
On some series involving the binomial coefficients
No full textUsing a simple transformation, we obtain much simpler forms for some series involving binomial coefficients derived by Necdet Batir. New evaluations are given and connections with Fibonacci numbers and the golden ratio are established. Finally we derive some Fibonacci and Lucas series involving the reciprocals of
On some series involving the binomial coefficients
Get PDFUsing a simple transformation, we obtain much simpler forms for some series
involving binomial coefficients derived by Necdet Batir. New
evaluations are given; and connections with Fibonacci numbers and the golden
ratio are established. Finally, we derive some Fibonacci and Lucas series
involving the reciprocals of .Comment: 17 page
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