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Bounds for Bateman's G-function and its applications

  • Mansour Mahmoud EMAIL logo and Ravi P. Agarwal
Published/Copyright: October 1, 2016
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Abstract

In this paper, we present an asymptotic formula for Bateman’s G-function G(x) and deduce the double inequality

12x2+3/2<G(x)-1x<12x2,x>0.

We apply this result to find estimates for the error term of the alternating series k=1(-1)k-1k+h, h-1,-2,-3,. Also, we study the monotonicity of some functions involving the function G(x). Finally, we propose a sharp double inequality for the function G(x) as a conjecture.

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Received: 2015-5-3
Accepted: 2015-11-20
Published Online: 2016-10-1
Published in Print: 2016-12-1

© 2016 by De Gruyter

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