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The p-k Gamma function

Some Inequalities Bounding Certain Ratios of the (p,k)-Gamma Function

Some Inequalities Bounding Certain Ratios of the (p,k)-Gamma Function

... Gautschi, Some elementary inequalities relating to the Gamma and incomplete Gamma function, Journal of Mathematics and Physics, 38(1)(1959), 77-81.. [4] A.[r] ...

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Convexity Properties and Inequalities Concerning the (p,k)-Gamma function

Convexity Properties and Inequalities Concerning the (p,k)-Gamma function

... differentiable function. Then f is a geometrically convex function if and only if the function xf f(x) 0 (x) is ...differentiable function. Then f is a geometrically convex function if ...

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New Two Parameter Gamma Function

New Two Parameter Gamma Function

... parameter Gamma function. Generalized p - k Gamma function is the deformation of the classical Gamma function, such that a p Γ k (x) ⇒ p Γ ...

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Vol 10, No 3 (2019)

Vol 10, No 3 (2019)

... sing p-k gamma function introduced by Gehlot (2017), a p-k gamma distribution with four parameters is constructed as a generalization of the p-k-gamma ...

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Some inequalities involving k gamma and k beta functions with applications   II

Some inequalities involving k gamma and k beta functions with applications II

... of k-special functions like the k-gamma function, the k-polygamma function, the k-beta function, the k-hypergeometric functions, solutions of ...

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SOME RESULTS ON THE $q,k$ AND $p,q$-GENERALIZED GAMMA FUNCTIONS

SOME RESULTS ON THE $q,k$ AND $p,q$-GENERALIZED GAMMA FUNCTIONS

... Euler’s Gamma function is one of the most important special func- tions with applications in many fields such as analysis, mathematical physics, statistics and probability ...q, k- generalized ...

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Relationships between Mahler Expansion and Higher Order q-Daehee polynomials

Relationships between Mahler Expansion and Higher Order q-Daehee polynomials

... and p-adic gamma function via Mahler ...weighted p-adic q-integrals of the derivative of p-adic gamma function related to the Stirling numbers of the both kinds and the ...

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The ith p affine surface area

The ith p affine surface area

... By the equality condition of the Blaschke-Santaló inequality (.) and Lemma ., equality holds in the inequality of Theorem . for i =  if and only if K is an ellipsoid, for  < i ≤ n –  if and only if ...

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Four Logarithmically Completely Monotonic Functions Involving Gamma Function and Originating from Problems of Traffic Flow

Four Logarithmically Completely Monotonic Functions Involving Gamma Function and Originating from Problems of Traffic Flow

... In this paper, two classes of functions, involving a parameter and the Euler gamma function, and two functions, involving the Euler gamma function, are verified to be logarithmically com[r] ...

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Windschitl type approximation formulas for the gamma function

Windschitl type approximation formulas for the gamma function

... the gamma function and Windschitl type approximation formulas have good properties, such as monotonicity and ...the gamma and factorial functions, but also provide a new proof of known inequalities ...

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Criterion of functional fullness in many-valued logic

Criterion of functional fullness in many-valued logic

... of function is full if the set contains any non-fictitious two-ary function taking all values and one- ary functions of closed minimal sets of some type (a set is closed if it generates only its functions ...

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Simple and Efficient Signature-based Consensus Protocol in the Asynchronous Distributed System

Simple and Efficient Signature-based Consensus Protocol in the Asynchronous Distributed System

... In the beginning of the Grouping_Consensus Task, each processor p k can use the SignConsensus function to obtain the local consensus value ( p k _Con ), list of faulty processors in [r] ...

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A new representation of extended Mittage-Leffler function and its properties

A new representation of extended Mittage-Leffler function and its properties

... contains Gamma function, Beta function, Hypergeometric function, Bessel’s function, Mittag-Leffler.. 14.[r] ...

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Padé approximant related to asymptotics for the gamma function

Padé approximant related to asymptotics for the gamma function

... 48. Mortici, C: On Ramanujan’s large argument formula for the gamma function. Ramanujan J. 26, 185-192 (2011) 49. Mortici, C: A continued fraction approximation of the gamma function. J. Math. ...

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Vol 1, No 3 (2010)

Vol 1, No 3 (2010)

... Since Pochhammer's symbol is associated with Gamma function and Gamma function is undefined for zero and negative integers therefore numerator and denominator parameters are adjusted in[r] ...

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New series involving the zeta function

New series involving the zeta function

... In [2, 3] Choi, Srivastava, and Quine used the theory of the double gamma function to evaluate some series associated with the zeta function. Now in the present paper, we use the property of the ...

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Monotonicity of the incomplete gamma function with applications

Monotonicity of the incomplete gamma function with applications

... From p =  and ...(x)/I p (x) is strictly decreasing on (, ∞). Therefore, R(a, p; x) is strictly decreasing on (, ∞), as follows from Lemma ...

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Monotonicity Results and Inequalities for the Gamma and Incomplete Gamma Functions

Monotonicity Results and Inequalities for the Gamma and Incomplete Gamma Functions

... differentiable function and p(t) 6≡ 0 an integrable nonnegative weight on the interval [a, b], if f 0 (t) and f 0 (t)/p(t) are integrable and both increasing or both decreasing, then for all real ...

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Monotonicity and inequalities for the gamma function

Monotonicity and inequalities for the gamma function

... Remark 3 In this paper, we investigate the monotonicity of the function f (x). In general, it is difficult to deal with such monotonicity since the gamma function occurs in denom- inator. However, by ...

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C=P K, where P = Plaintext, = Exclusive-Or, K =

C=P K, where P = Plaintext, = Exclusive-Or, K =

... randomness in cryptographic computations generates only a pseudo-random bit string. This combined with the issue of key distribution prevents unconditional or perfect secrecy (Upadhyay, G., & Nene, M. J. 2016) [4]. ...

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