본문 바로가기
KERD
논문KCI 등재

COMPLETE MONOTONICITY OF A FUNCTION INVOLVING THE TRI- AND TETRA-GAMMA FUNCTIONS

Q. Feng
장전수학회 (Jangjeon Mathematical Society)|2015.04|Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집) (Proceedings of the Jangjeon Mathematical Society)|제18권 제2호|pp. 253-264|DOI 10.17777/pjms.2015.18.2.012

2

조회

0

다운로드

0

인용

0

참고문헌

키워드

inequalitynecessary and sucient conditioncompletely monotonic functionpolygamma functionDescartes' sign rule
주제분류수학

초록

Abstract. The psi function ψ(x) is defined by ψ(x) = Γ'(x) / Γ(x) and ψ(i)(x) for i ∈ N denote polygamma functions, where Γ(x) is the gamma function. In the paper, the author proves that the function [ψ'(x)]2 + ψ''(x) - x2 + λx + 12 / 12x4(x + 1)2 is completely monotonic on (0,∞) if and only if λ ≥ 0, and so is its negative if and only if λ ≥ 4. From this, some inequalities are re ned and sharpened.

Abstract

Abstract. The psi function ψ(x) is defined by ψ(x) = Γ'(x) / Γ(x) and ψ(i)(x) for i ∈ N denote polygamma functions, where Γ(x) is the gamma function. In the paper, the author proves that the function [ψ'(x)]2 + ψ''(x) - x2 + λx + 12 / 12x4(x + 1)2 is completely monotonic on (0,∞) if and only if λ ≥ 0, and so is its negative if and only if λ ≥ 4. From this, some inequalities are re ned and sharpened.

참고문헌 (23)

  1. M. Abramowitz, "Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables" (1970)
  2. Horst Alzer, "Sharp inequalities for the digamma and polygamma functions", Forum Mathematicum, 16(2) (2004), Walter de Gruyter GmbH[DOI]
  3. Bai-Ni Guo, "A CLASS OF COMPLETELY MONOTONIC FUNCTIONS INVOLVING DIVIDED DIFFERENCES OF THE PSI AND TRI-GAMMA FUNCTIONS AND SOME APPLICATIONS", 대한수학회지, 48(3), pp.655~667 (2011), 대한수학회
  4. Bai-Ni Guo, "A completely monotonic function involving the tri-gamma function and with degree one", Applied Mathematics and Computation, 218(19), pp.9890~9897 (2012), Elsevier BV[DOI]
  5. Bai-Ni Guo, "Refinements of lower bounds for polygamma functions", Proceedings of the American Mathematical Society, 141(3), pp.1007~1015 (2013), American Mathematical Society (AMS)[DOI]
  6. Bai-Ni Guo, "Some uniqueness results for the non-trivially complete monotonicity of a class of functions involving the polygamma and related functions", Integral Transforms and Special Functions, 21(11), pp.849~858 (2010), Informa UK Limited[DOI]
  7. Bai-Ni Guo, "A completely monotonic function involving the tri- and tetra-gamma functions", Mathematica Slovaca, 63(3) (2013), Walter de Gruyter GmbH[DOI]
  8. D. S. Mitrinovic, "Analytic Inequalities" (1970), Springer-Verlag
  9. D. S. Mitrinovic, "Classical and New Inequalities in Analysis" (1993), Kluwer Academic Publishers
  10. F. Qi, "A method of constructing inequalities about ex", Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat., 8, pp.16~23 (1997)
  11. F. Qi, "Bounds for the ratio of two gamma functions", J. Inequal. Appl, 2010, pp.493058~ (2010)[DOI]
  12. Feng Qi, "Bounds for the Ratio of Two Gamma Functions: from Gautschi’s and Kershaw’s Inequalities to Complete Monotonicity", Turkish Journal of Analysis and Number Theory, 2(5), pp.152~164 (2014), Science and Education Publishing Co., Ltd.[DOI]
  13. "Completely monotonic degree of a function involving the tri- and tetra-gamma functions"[URL]
  14. "Complete monotonicity of a family of functions involving the tri- and tetra-gamma functions"[URL]
  15. Feng Qi, "Complete monotonicity of functions involving the $$q$$ q -trigamma and $${q}$$ q -tetragamma functions", Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 109(2), pp.419~429 (2015), Springer Nature[DOI]
  16. FENG QI, "COMPLETE MONOTONICITY OF A FUNCTION INVOLVING THE DIVIDED DIFFERENCE OF PSI FUNCTIONS", Bulletin of the Australian Mathematical Society, 88(02), pp.309~319 (2013), Cambridge University Press (CUP)[DOI]
  17. Feng Qi, "Completely monotonic functions involving divided differences of the di- and tri-gamma functions and some applications", Communications on Pure and Applied Analysis, 8(6), pp.1975~1989 (2009), American Institute of Mathematical Sciences (AIMS)[DOI]
  18. Feng Qi, "Necessary and sufficient conditions for functions involving the tri- and tetra-gamma functions to be completely monotonic", Advances in Applied Mathematics, 44(1), pp.71~83 (2010), Elsevier BV[DOI]
  19. F. Qi, "Bounds for the ratio of two gamma functions|From Wen-del's and related inequalities to logarithmically completely monotonic functions", Banach J. Math. Anal., 6(2), pp.132~158 (2012)
  20. Feng Qi, "Bounds for the ratio of two gamma functions: from Wendel’s asymptotic relation to Elezović-Giordano-Pečarić’s theorem", Journal of Inequalities and Applications, 2013(1), pp.542~ (2013), Springer Nature[DOI]
  21. Feng Qi, "Complete monotonicity of a function involving the divided difference of digamma functions", Science China Mathematics, 56(11), pp.2315~2325 (2013), Springer Nature[DOI]
  22. D. V. Widder, "The Laplace Transform" (1946), Princeton University Press
  23. Jiao-Lian Zhao, "Complete monotonicity of two functions involving the tri-and tetra-gamma functions", Periodica Mathematica Hungarica, 65(1), pp.147~155 (2012), Springer Nature[DOI]

관련 논문AI추천

Some completely monotonic functions involving the gamma and polygamma functionsAi-Jun Li, Chao-Ping Chen대한수학회 · 대한수학회지2008 · 제45권 제1호Inequalities and complete monotonicity for the gamma and related functions최준상, Chao-Ping Chen대한수학회 · 대한수학회논문집2019 · 제34권 제4호TWO NEW PROOFS OF THE COMPLETE MONOTONICITY OF A FUNCTION INVOLVING THE PSI FUNCTIONBai-Ni Guo, Feng Qi대한수학회 · 대한수학회보2010 · 제47권 제1호COMPLETELY MONOTONIC FUNCTIONS RELATING TO THE GAMMA AND PSI FUNCTIONSX. Li장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2009 · 제12권 제1호NEW COMPLETE MONOTONICITY PROPERTIES OF THE GAMMA FUNCTIONBatir장전수학회 · Advanced Studies in Contemporary Mathematics2009 · 제19권 제2호MONOTONICITY CRITERION AND FUNCTIONAL INEQUALITIES FOR SOME q-SPECIAL FUNCTIONSKhaled Mehrez대한수학회 · 대한수학회지2021 · 제58권 제1호

이 간행물의 다른 논문 (11건)

A QUALITATIVE RESULT CONCERNING QUASIREPRESENTATIONS OF COMPACT GROUPSA. I. Shternpp. 139-143EXAMPLES OF NON-DIFFERENTIABILITY POINTS OF RIESZ-NÁGY-TAKÁCS FUNCTION백인수pp. 145-151THE ANALYSIS OF STUDENTS’ SURVEY FOR THE CHANGE OF SECONDARY SCHOOL TEACHERS’ TEACHING BEHAVIOR BASED ON SELF-REFLECTIONJ. Kwonpp. 153-163THE DIFFERENCE BETWEEN THE APPROXIMATE AND THE ACCURATE SOLUTION TO STOCHASTIC DIFFERENTIAL DELAY EQUATION김영호pp. 165-175A symmetric identity on the q-Genocchi polynomials of higher-order under third dihedral group D3M. Acikgoz, S. Araci, E. Agyüzpp. 177-187
원문 보기