논문KCI 등재
An inequality for the generalized-Euler-constant function
0
조회
0
다운로드
3
인용
0
참고문헌
주제분류수학
초록
Letx,y∈(0,1] and x .= y. This article proves that for all integers k ≥0,γ(k+1) (I(x,y) <γ(k)(x)γ(k)(y)x y< γ(k+1) (max(x,y) ,where I(x,y) is the exponential mean of two positive numbers x and y, and γ(z) is the generalized-Euler-constant function, defined byγ(z) =∞. n =1zn 1.1nlog n + 1n.
Abstract
Letx,y∈(0,1] and x .= y. This article proves that for all integers k ≥0,γ(k+1) (I(x,y) <γ(k)(x)γ(k)(y)x y< γ(k+1) (max(x,y) ,where I(x,y) is the exponential mean of two positive numbers x and y, and γ(z) is the generalized-Euler-constant function, defined byγ(z) =∞. n =1zn 1.1nlog n + 1n.
참고문헌 (5)
- J. Sondowa, "The generalized-Euler-constant function (z) and a generalization of Somoss quadratic recurrence constant", J. Math. Anal. Appl, 332, pp.292~314 (2007)
- J. Sondow, "Double integrals for Eulers constant and ln(4", ) and an analog of Hadjicostass formula, 2005, pp.112, 61~65
- "New Vacca-type rational series for Eulers constant and its alternating analog ln(4/), preprint"[URL]
- K.B. Stolarsky, "Generalizations of the logarithmic mean", Math. Mag, 48, pp.87~92 (1975)
- K.B. STOLARSKY, "The power and generalized logarithmic means", Amer. Math. Monthly, 87, pp.545~548 (1980)
관련 논문AI추천
Inequalities and complete monotonicity for the gamma and related functions최준상, Chao-Ping Chen대한수학회 · 대한수학회논문집2019 · 제34권 제4호Some completely monotonic functions involving the gamma and polygamma functionsAi-Jun Li, Chao-Ping Chen대한수학회 · 대한수학회지2008 · 제45권 제1호COMPLETE MONOTONICITY OF A FUNCTION INVOLVING THE TRI- AND TETRA-GAMMA FUNCTIONSQ. Feng장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2015 · 제18권 제2호THE LOG-CONVEXITY OF ANOTHER CLASS OF ONE-PARAMETER MEANS AND ITS APPLICATIONSZhen-Hang Yang대한수학회 · 대한수학회보2012 · 제49권 제1호TWO NEW PROOFS OF THE COMPLETE MONOTONICITY OF A FUNCTION INVOLVING THE PSI FUNCTIONBai-Ni Guo, Feng Qi대한수학회 · 대한수학회보2010 · 제47권 제1호Certain integral representations of Generalized Stieltjes constants γk(a)신종문영남수학회 · East Asian Mathematical Journal2015 · 제31권 제1호
이 간행물의 다른 논문 (9건)
Second preduals of tridual von Neumann algebras are geometrically uniqueA. I. Shternpp. 1-8Note on q-Genocchi numbers and polynomialsT. Kimpp. 9-15The isomorphism between two fundamental groups by Cayley graphs˙I. Naci Cang¨ul, A. Sinan C¸ evik, ¨Ozden Koruo˘glupp. 17-23Weakly biased maps and common fixed point theorems under rational inequalityG. V. R. Babu, M. V. R. Kameswaripp. 25-39On solvability and stability of solutions of linear integral and summary equations of the first kindT. K. Yuldashevpp. 41-56