In the present paper, we give two new proofs for the necessary and sufficient condition α ≤ 1 such that the function xα[ln x − ψ(x)] is completely monotonic on (0,∞).
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https://www.riss.kr/link?id=A103364228
Bai-Ni Guo (Henan Polytechnic University) ; Feng Qi (Tianjin Polytechnic University)
2010
English
KCI등재,SCIE,SCOPUS
학술저널
103-111(9쪽)
29
0
상세조회0
다운로드다국어 초록 (Multilingual Abstract)
In the present paper, we give two new proofs for the necessary and sufficient condition α ≤ 1 such that the function xα[ln x − ψ(x)] is completely monotonic on (0,∞).
In the present paper, we give two new proofs for the necessary and sufficient condition α ≤ 1 such that the function xα[ln x − ψ(x)] is completely monotonic on (0,∞).
참고문헌 (Reference)
1 F. Qi, "Three classes of logarithmically completely monotonic functions involving gamma and psi functions" 18 (18): 503-509, 2007
2 D. V. Widder, "The Laplace Transform" Princeton University Press 1941
3 R. D. Atanassov, "Some properties of a class of logarithmically completely monotonic functions" 41 (41): 21-23, 1988
4 H. Minc, "Some inequalities involving (r!)1/r" 14 (14): 41-46, 1965
5 F. Qi, "Some completely monotonic functions involving the gamma and polygamma functions" 80 (80): 81-88, 2006
6 F. Qi, "Some completely monotonic functions involving polygamma functions and an application" 310 (310): 303-308, 2005
7 Feng Qi, "SOME LOGARITHMICALLY COMPLETELY MONOTONIC FUNCTIONS RELATED TO THE GAMMA FUNCTION" 대한수학회 47 (47): 1283-1297, 2010
8 B.-N. Guo, "Refinements and sharpenings of some double inequalities for bounding the gamma function"
9 H. Alzer, "On some inequalities for the gamma and psi functions" 66 (66): 373-389, 1997
10 A.-Q. Liu, "Monotonicity and logarithmic concavity of two functions involving exponential function" 39 (39): 686-691, 2008
1 F. Qi, "Three classes of logarithmically completely monotonic functions involving gamma and psi functions" 18 (18): 503-509, 2007
2 D. V. Widder, "The Laplace Transform" Princeton University Press 1941
3 R. D. Atanassov, "Some properties of a class of logarithmically completely monotonic functions" 41 (41): 21-23, 1988
4 H. Minc, "Some inequalities involving (r!)1/r" 14 (14): 41-46, 1965
5 F. Qi, "Some completely monotonic functions involving the gamma and polygamma functions" 80 (80): 81-88, 2006
6 F. Qi, "Some completely monotonic functions involving polygamma functions and an application" 310 (310): 303-308, 2005
7 Feng Qi, "SOME LOGARITHMICALLY COMPLETELY MONOTONIC FUNCTIONS RELATED TO THE GAMMA FUNCTION" 대한수학회 47 (47): 1283-1297, 2010
8 B.-N. Guo, "Refinements and sharpenings of some double inequalities for bounding the gamma function"
9 H. Alzer, "On some inequalities for the gamma and psi functions" 66 (66): 373-389, 1997
10 A.-Q. Liu, "Monotonicity and logarithmic concavity of two functions involving exponential function" 39 (39): 686-691, 2008
11 Bai-Ni Guo, "MONOTONICITY AND LOGARITHMIC CONVEXITY OF THREE FUNCTIONS INVOLVING EXPONENTIAL FUNCTION" 한국수학교육학회 15 (15): 387-392, 2008
12 Ch.-P. Chen, "Logarithmically completely monotonic functions relating to the gamma function" 321 (321): 405-411, 2006
13 C. Berg, "Integral representation of some functions related to the gamma function" 1 (1): 433-439, 2004
14 G. D. Anderson, "Inequalities for zero-balanced hypergeometric functions" 347 (347): 1713-1723, 1995
15 M. Abramowitz, "Handbook of mathematical functions with formulas, graphs, and mathematical tables, National Bureau of Standards Applied Mathematics Series, 55 Superintendent of Documents" U.S. Government Printing Office 1965
16 A. Z. Grinshpan, "Completely monotonic functions involving the gamma and q-gamma functions" 134 (134): 1153-1160, 2006
17 F. Qi, "Complete monotonicities of functions involving the gamma and digamma functions" 7 (7): 63-72, 2004
18 F. Qi, "Bounds for the ratio of two gamma functions"
19 L. Gordon, "A stochastic approach to the gamma function" 101 (101): 858-865, 1994
20 Sh.-Q. Zhang, "A concise proof for properties of three functions involving the exponential function" 9 : 177-183, 2009
21 F. Qi, "A complete monotonicity property of the gamma function" 296 (296): 603-607, 2004
NONTRIVIAL SOLUTIONS FOR BOUNDARY-VALUE PROBLEMS OF NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS
TWO NEW PROOFS OF THE COMPLETE MONOTONICITY OF A FUNCTION INVOLVING THE PSI FUNCTION
A CHARACTERIZATION OF M-HARMONICITY
학술지 이력
연월일 | 이력구분 | 이력상세 | 등재구분 |
---|---|---|---|
2023 | 평가예정 | 해외DB학술지평가 신청대상 (해외등재 학술지 평가) | |
2020-01-01 | 평가 | 등재학술지 유지 (해외등재 학술지 평가) | |
2010-01-01 | 평가 | 등재학술지 유지 (등재유지) | |
2008-01-01 | 평가 | 등재학술지 유지 (등재유지) | |
2006-01-01 | 평가 | 등재학술지 유지 (등재유지) | |
2004-01-01 | 평가 | 등재학술지 유지 (등재유지) | |
2001-07-01 | 평가 | 등재학술지 선정 (등재후보2차) | |
1999-01-01 | 평가 | 등재후보학술지 선정 (신규평가) |
학술지 인용정보
기준연도 | WOS-KCI 통합IF(2년) | KCIF(2년) | KCIF(3년) |
---|---|---|---|
2016 | 0.35 | 0.1 | 0.27 |
KCIF(4년) | KCIF(5년) | 중심성지수(3년) | 즉시성지수 |
0.23 | 0.2 | 0.339 | 0.04 |