Polygamma function
Logarithmically Completely Monotonic Functions Involving Gamma and Polygamma Functions
... [14] F. Qi, B.-N. Guo, and Ch.-P. Chen, Some completely monotonic functions involving the gamma and polygamma functions, J. Austral. Math. Soc. 79 (2006), no. 1, in press. RGMIA Res. Rep. Coll. 7 (2004), no. 1, ...
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Certain Inequalities for the Conformable Gamma and Polygamma Functions
... Abstract. In a recent paper, Sarikaya et al. introduced a new analogue of the classical Gamma function which they called, the conformable Gamma function. Motivated by their results, this paper seeks to ...
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Some inequalities involving the polygamma functions
... 5. Alzer, H., Wells, J.: Inequalities for the polygamma functions. SIAM J. Math. Anal. 29(6), 1459–1466 (1998) 6. Alzer, H.: On some inequalities for the gamma and psi functions. Math. Comput. 66(217), 373–389 ...
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Complete monotonicity related to the k polygamma functions with applications
... and polygamma functions play an important role in the theory of special functions, and are closely related to factorial, fractional differential equations, mathematical physics and crops up in many unexpected place ...
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Certain relationships among polygamma functions, Riemann zeta function and generalized zeta function
... among polygamma functions, Riemann zeta function, and generalized zeta function by mainly modifying Chen’s method ...lambda function λ(s) defined ...
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Some completely monotonic functions involving the polygamma functions
... the polygamma functions in the liter- ature, many of which are closely related to the fact that ψ is completely monotonic on (0, + ∞ ...a function f (x) is said to be completely monotonic on (a, b) if it ...
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A Completely Monotonic Function Involving Divided Differences of Psi and Polygamma Functions and an Application
... A function involving the divided differences of the psi function and the polygamma functions is proved to be completely ...a function originated from establishing the best upper and lower ...
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Some monotonicity properties and inequalities for the generalized digamma and polygamma functions
... the polygamma functions. The gamma, digamma and polygamma functions play an im- portant role in the theory of special functions, and have many applications in other many branches, such as statistics, ...
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Estimating the polygamma functions for negative integers
... Ozcag et al. [, ] applied the neutrix limit to extend the definition of incomplete beta function and its partial derivatives for negative integers. Also, the digamma function was generalized for negative ...
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6. Sums in Terms of Polygamma Functions
... The major aim of this paper is to investigate general binomial sums with various parameters that then enables one to give more general representations of (1.1) and (1.2), thereby general[r] ...
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Monotonicity of a mean related to polygamma functions with an application
... Qi, F: A class of logarithmically completely monotonic functions and application to the best bounds in the second Gautschi-Kershaw’s inequality.. Qi, F, Guo, B-N: A class of logarithmica[r] ...
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Some Completely Monotonic Functions Involving the Gamma and Polygamma Functions
... Hence, p 00 (t) increases in (0, ∞). Since p 00 (0) = 3 > 0, we have p 00 (t) > 0 and p 0 (t) is increasing. Because of p 0 (0) = 0, it follows that p 0 (t) > 0 in (0, ∞), and then p(t) is increasing. From p(0) ...
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Note on a Class of Completely Monotonic Functions Involving the Polygamma Functions
... Guo, T` esh¯ u H´ ansh` u G` ail` un ( A Panorama of Special Functions ), The Series of Advanced Physics of Peking University, Peking University Press, Beijing, China, 2000. Widder, The [r] ...
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Two Class of Completely Monotonic Functions Involving Gamma and Polygamma Functions
... To the best of our knowledge, the notion or terminology “logarithmically com- pletely monotonic function” was introduced explicitly in [9], published formally in [8], and used immediately in [2, 4, 10, 11, 12]. ...
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A Double Inequality for Divided Differences and Some Identities of Psi and Polygamma Functions
... gamma function Γ(x) plays a cen- tral role in the theory of special functions and has much extensive applications in many branches, for example, statistics, physics, engineering, and other mathemati- cal ...
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A Class of Logarithmically Completely Monotonic Functions Associated with a Gamma Function
... Recently, the completely monotonic or logarithmically completely monotonic func- tions have been the subject of intensive research. In particular, many remarkable results for the complete monotonicity or logarithmically ...
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The Best Bounds in Gautschi-Kershaw Inequalities
... Abstract. By employing the convolution theorem of Laplace transforms, some asymptotic formulas and integral representations of the gamma, psi and polygamma functions, and other analytic techniques, this note ...
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Some inequalities involving k gamma and k beta functions with applications II
... k-gamma function, the k-polygamma function, the k-beta function, the k-hypergeometric functions, solutions of k-hypergeometric differential equations, contiguous functions relations, ...
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On complete monotonicity for several classes of functions related to ratios of gamma functions
... gamma function Γ (x) and polygamma functions ψ (i) (x) for i ≥ 0 are of the recurrent period 1, that is, the recurrence relations Γ (x + 1) = xΓ (x) and ...and polygamma functions Γ (x) and ψ (i) ...
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Neutrix Limit on Divergent Series
... the polygamma function [2], the q- analogue of the incomplete gamma function [3], the delta function [4, 5], the q-gamma function [6], quantum field theory [7], the beta function ...
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