Generalized Statistically Almost Convergence Based on the Difference Operator which Includes the (p, q)-Gamma Function and Related Approximation Theorems
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DOI: 10.1007/s00025-018-0789-6
Abstract: This paper is devoted to extend the notion of almost convergence and its statistical forms with respect to the difference operator involving (p, q)-gamma function and an increasing sequence $$(\lambda _n)$$(λn) of positive numbers. We firstly… read more here.
Keywords: difference operator; almost convergence; gamma function; delta alpha ... See more keywords
ON ALGEBRAIC DIFFERENTIAL EQUATIONS FOR THE GAMMA FUNCTION AND -FUNCTIONS IN THE EXTENDED SELBERG CLASS
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DOI: 10.1017/s000497271700020x
Abstract: This paper concerns the problem of algebraic differential independence of the gamma function and ${\mathcal{L}}$ -functions in the extended Selberg class. We prove that the two kinds of functions cannot satisfy a class of algebraic… read more here.
Keywords: class; extended selberg; algebraic differential; gamma function ... See more keywords
Properties and Applications of a New Extended Gamma Function Involving Confluent Hypergeometric Function
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DOI: 10.1155/2021/2491248
Abstract: In this paper, a new confluent hypergeometric gamma function and an associated confluent hypergeometric Pochhammer symbol are introduced. We discuss some properties, for instance, their different integral representations, derivative formulas, and generating function relations. Different… read more here.
Keywords: function; properties applications; confluent hypergeometric; gamma function ... See more keywords
Some inequalities involving the extended gamma function and the Kummer confluent hypergeometric k-function
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DOI: 10.1186/s13660-018-1717-8
Abstract: In the paper, the authors present some inequalities involving the extended gamma function and the Kummer confluent hypergeometric k-function via some classical inequalities such as Chebychev’s inequality for synchronous (or asynchronous, respectively) mappings, give a… read more here.
Keywords: confluent hypergeometric; kummer confluent; hypergeometric function; gamma function ... See more keywords
Some Extensions of the Prabhu-Srivastava Theorem Involving the (p,q)-Gamma Function
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DOI: 10.2298/fil1714507l
Abstract: In this paper, we obtain some limit formulas for derivatives of (p,q)-gamma function and (p,q)-digamma function at their poles. These limit formulas extend the Prabhu-Srivastava theorem involving gamma function and digamma function. read more here.
Keywords: involving gamma; theorem involving; prabhu srivastava; srivastava theorem ... See more keywords
An Asymptotic Expansion for the Generalized Gamma Function
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DOI: 10.3390/sym14071412
Abstract: The symmetric patterns that inequalities contain are reflected in researchers’ studies in many mathematical sciences. In this paper, we prove an asymptotic expansion for the generalized gamma function Γμ(v) and study the completely monotonic (CM)… read more here.
Keywords: gamma function; function; asymptotic expansion; generalized gamma ... See more keywords
On Some Bounds for the Gamma Function
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DOI: 10.3390/sym15040937
Abstract: Both theoretical and applied mathematics depend heavily on inequalities, which are rich in symmetries. In numerous studies, estimations of various functions based on the characteristics of their symmetry have been provided through inequalities. In this… read more here.
Keywords: bounds gamma; gamma function;
On algebraic differential equations of gamma function and Riemann zeta function
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DOI: 10.5186/aasfm.2019.4455
Abstract: Abstract. Due to Voronin’s universality theorem and Riemann–von Mangoldt formula, this paper concerns the problem of algebraic differential independence between the gamma function Γ and the function f(ζ), where ζ is the Riemann zeta function… read more here.
Keywords: gamma function; algebraic differential; riemann; riemann zeta ... See more keywords
A complete monotonicity property of the multiple gamma function
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DOI: 10.5802/crmath.115
Abstract: We consider the following functions fn (x) = 1− ln x + lnGn (x +1) x and gn (x) = x Gn (x +1) x , x ∈ (0,∞), n ∈N, where Gn (z) =… read more here.
Keywords: complete monotonicity; completely monotonic; gamma function; function ... See more keywords