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On some inequalities for the gamma and psi functions
 MATH. COMP
, 1997
"... We present new inequalities for the gamma and psi functions, and we provide new classes of completely monotonic, starshaped, and superadditive functions which are related to Γ and ψ. Euler’s gamma function Γ(x) = ..."
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Cited by 78 (3 self)
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We present new inequalities for the gamma and psi functions, and we provide new classes of completely monotonic, starshaped, and superadditive functions which are related to Γ and ψ. Euler’s gamma function Γ(x) =
A completely monotonic function involving divided differences of psi and polygamma functions and an application
 RGMIA Res. Rep. Coll
"... Abstract. A class of functions involving the divided differences of the psi function and the polygamma functions and originating from Kershaw’s double inequality are proved to be completely monotonic. As applications of these results, the monotonicity and convexity of a function involving ratio of t ..."
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Cited by 37 (25 self)
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Abstract. A class of functions involving the divided differences of the psi function and the polygamma functions and originating from Kershaw’s double inequality are proved to be completely monotonic. As applications of these results, the monotonicity and convexity of a function involving ratio of two gamma functions and originating from establishment of the best upper and lower bounds in Kershaw’s double inequality are derived, two sharp double inequalities involving ratios of double factorials are recovered, the probability integral or error function is estimated, a double inequality for ratio of the volumes of the unit balls in R n−1 and R n respectively is deduced, and a symmetrical upper and lower bounds for the gamma function in terms of the psi function is generalized. 1.
The Incomplete Gamma Functions Since Tricomi
 In Tricomi's Ideas and Contemporary Applied Mathematics, Atti dei Convegni Lincei, n. 147, Accademia Nazionale dei Lincei
, 1998
"... The theory of the incomplete gamma functions, as part of the theory of conuent hypergeometric functions, has received its rst systematic exposition by Tricomi in the early 1950s. His own contributions, as well as further advances made thereafter, are surveyed here with particular emphasis on asy ..."
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Cited by 27 (1 self)
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The theory of the incomplete gamma functions, as part of the theory of conuent hypergeometric functions, has received its rst systematic exposition by Tricomi in the early 1950s. His own contributions, as well as further advances made thereafter, are surveyed here with particular emphasis on asymptotic expansions, zeros, inequalities, computational methods, and applications.
SOME PROPERTIES OF THE GAMMA AND PSI FUNCTIONS, WITH APPLICATIONS
"... Abstract. In this paper, some monotoneity and concavity properties of the gamma, beta and psi functions are obtained, from which several asymptotically sharp inequalities follow. Applying these properties, the authors improve some wellknown results for the volume Ωn of the unit ball B n ⊂ R n,thesu ..."
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Cited by 15 (0 self)
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Abstract. In this paper, some monotoneity and concavity properties of the gamma, beta and psi functions are obtained, from which several asymptotically sharp inequalities follow. Applying these properties, the authors improve some wellknown results for the volume Ωn of the unit ball B n ⊂ R n,thesurface area ωn−1 of the unit sphere S n−1, and some related constants. 1.
On Some Inequalities for the Gamma Function
"... We present some elementary proofs of wellknown inequalities for the gamma function and for the ratio of two gamma functions. The paper is purely expository and it is based on the talk that the first author gave during the memorial conference in Patras, 2012. AMS Subject Classifications: 33B15, 26D0 ..."
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We present some elementary proofs of wellknown inequalities for the gamma function and for the ratio of two gamma functions. The paper is purely expository and it is based on the talk that the first author gave during the memorial conference in Patras, 2012. AMS Subject Classifications: 33B15, 26D07.
Diameter and Rumour Spreading in RealWorld Network Models
"... I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis, including any required final revisions, as accepted by my examiners. I understand that my thesis may be made electronically available to the public. ii The socalled ‘smallworld phenomenon’, observed in ma ..."
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I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis, including any required final revisions, as accepted by my examiners. I understand that my thesis may be made electronically available to the public. ii The socalled ‘smallworld phenomenon’, observed in many realworld networks, is that there is a short path between any two nodes of a network, whose length is much smaller that the network’s size, typically growing as a logarithmic function. Several mathematical models have been defined for social networks, the WWW, etc., and this phenomenon translates to proving that such models have a small diameter. In the first part of this thesis, we rigorously analyze the diameters of several random graph classes that are introduced specifically to model complex networks, verifying whether this phenomenon occurs in them. In Chapter 3 we develop a versatile technique for proving upper bounds for diameters of evolving random graph models, which is based on defining a coupling between these models and variants of random recursive trees. Using this technique we prove, for the first time,
Authors ’ Note
"... Most of the errors in the original paper had to do with saying that certain functions related to the qgamma function were not completely monotonic. We discovered these errors through reading the paper Some completely monotonic functions involving the qgamma function, by Peng Gao, ..."
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Most of the errors in the original paper had to do with saying that certain functions related to the qgamma function were not completely monotonic. We discovered these errors through reading the paper Some completely monotonic functions involving the qgamma function, by Peng Gao,
1Transmission Capacity of Adhoc Networks with Multiple Antennas using Transmit Stream Adaptation and Interference Cancelation
"... The transmission capacity of an adhoc network is the maximum density of active transmitters per unit area, given an outage constraint at each receiver for a fixed rate of transmission. Assuming that the transmitter locations are distributed as a Poisson point process, this paper derives upper and l ..."
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The transmission capacity of an adhoc network is the maximum density of active transmitters per unit area, given an outage constraint at each receiver for a fixed rate of transmission. Assuming that the transmitter locations are distributed as a Poisson point process, this paper derives upper and lower bounds on the transmission capacity of an adhoc network when each node is equipped with multiple antennas. The transmitter either uses eigen multimode beamforming or a subset of its antennas to transmit multiple data streams, while the receiver uses partial zero forcing to cancel certain interferers using some of its spatial receive degrees of freedom (SRDOF). The receiver either cancels the nearest interferers or those interferers that maximize the postcancelation signaltointerference ratio. Using the obtained bounds, the optimal number of data streams to transmit, and the optimal SRDOF to use for interference cancelation are derived that provide the best scaling of the transmission capacity with the number of antennas. With beamforming, single data stream transmission together with using all but one SRDOF for interference cancelation is optimal, while without beamforming, single data stream transmission together with using a fraction of the total SRDOF for interference cancelation is optimal. I.