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On the Formalization of Gamma Function in HOL
Journal of Automated Reasoning, 2014zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Umair Siddique, Osman Hasan
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Numerical Algorithms, 2008
Some new inequalities for Euler's gamma function are derived and proved.
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Some new inequalities for Euler's gamma function are derived and proved.
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Rendiconti del Circolo Matematico di Palermo, 1999
Inequalities and convexity properties known for the gamma function are extended to the qgamma function, 0<q<1 . Applying some classical inequalities for convex functions, we deduce monotonicity results for several functions involving the qgamma function. Further applications to the probability theory are given.
Elezović, N. +2 more
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Inequalities and convexity properties known for the gamma function are extended to the qgamma function, 0<q<1 . Applying some classical inequalities for convex functions, we deduce monotonicity results for several functions involving the qgamma function. Further applications to the probability theory are given.
Elezović, N. +2 more
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Completely monotonic functions related to the gamma and the q-gamma functions
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2016zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Continued Fraction Approximation for the Gamma Function by the Tri-gamma Function
Results in Mathematics, 2017zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On the functional equations of the q-Gamma function
Aequationes mathematicae, 2014A functional equation is a relationship between values of a function with different arguments. The author mentions some classical functional relations of the gamma function and \(q\)-gamma function. \textit{E. Artin} [The gamma function. New York-Chicago-San Francisco-Toronto-London: Holt, Rinehart and Winston (1964; Zbl 0144.06802)] provides a ...
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1976
Artykuł w: Annales Universitatis Mariae Curie-Skłodowska. Sectio A, Mathematica. Vol. 28 (1974), s. 53-58 ; streszcz. pol., ros. ; Artykuł w: Annales Universitatis Mariae Curie-Skłodowska. Sectio A, Mathematica. Vol. 28 (1974), s. 53-58 ; streszcz. pol., ros.
Lewandowski, Zdzisław (1929-2011) +2 more
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Artykuł w: Annales Universitatis Mariae Curie-Skłodowska. Sectio A, Mathematica. Vol. 28 (1974), s. 53-58 ; streszcz. pol., ros. ; Artykuł w: Annales Universitatis Mariae Curie-Skłodowska. Sectio A, Mathematica. Vol. 28 (1974), s. 53-58 ; streszcz. pol., ros.
Lewandowski, Zdzisław (1929-2011) +2 more
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2004
We have defined (Set Theory, III, p. 179) the function n! for every integer n ≥ 0, as equal to the product \(\prod\limits_{0 \leqslant k \leqslant n} {(n - k)}\); so 0!=1 and (n+1)!=(n+1)n! for n ≥ 0. We set г(n) = (n − 1)! for each integer n ≥ 1; we propose to define, on the set of real numbers x > 0, a continuous function г(x) extending the function ...
Elementary Theory, Philip Spain
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We have defined (Set Theory, III, p. 179) the function n! for every integer n ≥ 0, as equal to the product \(\prod\limits_{0 \leqslant k \leqslant n} {(n - k)}\); so 0!=1 and (n+1)!=(n+1)n! for n ≥ 0. We set г(n) = (n − 1)! for each integer n ≥ 1; we propose to define, on the set of real numbers x > 0, a continuous function г(x) extending the function ...
Elementary Theory, Philip Spain
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Extended k-Gamma and k-Beta Functions of Matrix Arguments
Mathematics, 2020Praveen Agarwal +2 more
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