On Qi’s Normalized Remainder of Maclaurin Power Series Expansion of Logarithm of Secant Function
Copyright policy )On Qi’s Normalized Remainder of Maclaurin Power Series Expansion of Logarithm of Secant Function
In the study, the authors introduce Qi’s normalized remainder of the Maclaurin power series expansion of the function lnsecx=−lncosx; in view of a monotonicity rule for the ratio of two Maclaurin power series and by virtue of the logarithmic convexity of the function (2x−1)ζ(x) on (1,∞), they prove the logarithmic convexity of Qi’s normalized remainder; with the aid of a monotonicity rule for the ratio of two Maclaurin power series, the authors present the monotonic property of the ratio between two Qi’s normalized remainders.
- Henan Polytechnic University China (People's Republic of)
- National Kaohsiung Normal University (高雄師範大學) Taiwan
- Hulunbuir University China (People's Republic of)
- National Kaohsiung Normal University Taiwan
Maclaurin power series expansion, Qi’s normalized remainder, QA1-939, Riemann zeta function, Bernoulli number, Dirichlet eta function, Mathematics, Stirling number of the second kind
Maclaurin power series expansion, Qi’s normalized remainder, QA1-939, Riemann zeta function, Bernoulli number, Dirichlet eta function, Mathematics, Stirling number of the second kind
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