polygamma functions
Some completely monotonic functions involving the polygamma functions
... There are many interesting inequalities involving the polygamma functions in the liter- ature, many of which are closely related to the fact that ψ is completely monotonic on (0, + ∞ ). Here we recall that ...
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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 ...
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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 ...
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Certain Inequalities for the Conformable Gamma and Polygamma Functions
... Recently, Sarikaya et al. [10] introduced a new analogue of the Gamma func- tion which they called the conformable Gamma function. Motivated by their results, we have established some inequalities involving the ...
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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 ...
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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 integers by ...
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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. ...
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A Completely Monotonic Function Involving Divided Differences of Psi and Polygamma Functions and an Application
... Abstract. A function involving the divided differences of the psi function and the polygamma functions is proved to be completely monotonic. As an appli- cation of this result, the monotonicity and ...
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Certain relationships among polygamma functions, Riemann zeta function and generalized zeta function
... Many useful and interesting properties, identities, and relations for the Riemann zeta function ζ (s) and the Hurwitz zeta function ζ (s,a) have been developed. Here, we aim at giving certain (presumably) new and ...
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A Double Inequality for Divided Differences and Some Identities of Psi and Polygamma Functions
... [9] F. Qi and B.-N. Guo, Wendel-Gautschi-Kershaw’s inequalities and sufficient and necessary conditions that a class of functions involving ratio of gamma functions are logarithmically completely monotonic, ...
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Two Class of Completely Monotonic Functions Involving Gamma and Polygamma Functions
... [1] M. Abramowitz and I.A. Stegun (Eds), Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Reprint of the 1972 edition. A Wiley-Interscience Pub- lication. Selected Government ...
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6. Sums in Terms of Polygamma Functions
... Coffey [8] also constructs new integral representations for these sums. The major aim of this paper is to investigate general binomial sums with various parameters that then enables one to give more general ...
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Some Completely Monotonic Functions Involving the Gamma and Polygamma Functions
... [4] F. Guo, Complete monotonicities of functions involving the gamma and digamma functions, RGMIA Res. Available online at http://rgmia. Qi) Department of Applied Mathematics and Informa[r] ...
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Note on a Class of Completely Monotonic Functions Involving the Polygamma Functions
... [1] M. Abramowitz and I. A. Stegun (Eds), Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Reprint of the 1972 edition. A Wiley-Interscience Pub- lication. Selected Government ...
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Monotonicity of a mean related to polygamma functions with an application
... f is called logarithmically completely monotonic on an interval I if f has derivatives of all orders on I and its logarithm ln f satisfies (–) n (ln f (x)) (n) ≥ for all n ∈ N on I (see []). For convenience, we ...
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The Best Bounds in Gautschi-Kershaw Inequalities
... [16] 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 ...
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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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On complete monotonicity for several classes of functions related to ratios of gamma functions
... 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) (x), one can ...
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Importance of functional programming Assigning functions to variables, arrays, and other data structures Passing functions to other functions Returning functions from functions Making anonymous functions Capturing local variables (making closures) Using the apply and call methods
... Can assign functions to variables Can put functions in arrays or other data structures Can pass functions to other functions Can return functions from functions Can create functions with[r] ...
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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 [8], the gamma function [9] and ...
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