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The history of qcalculus and a new method
, 2000
"... 1.1. Partitions, generalized Vandermonde determinants and representation theory. 5 1.2. The Frobenius character formulae. 8 ..."
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1.1. Partitions, generalized Vandermonde determinants and representation theory. 5 1.2. The Frobenius character formulae. 8
Some monotonicity properties of gamma and qgamma functions, Available onlie at http://arxiv.org/abs/0709.1126v2
"... Abstract. We prove some properties of completely monotonic functions and apply them to obtain results on gamma and qgamma functions. 1. ..."
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Abstract. We prove some properties of completely monotonic functions and apply them to obtain results on gamma and qgamma functions. 1.
Characterization theorems for the Gneiting class of space–time covariances
"... We characterize the Gneiting class of space–time covariance functions and give more relaxed conditions on the functions involved. We then show necessary conditions for the construction of compactly supported functions of the Gneiting type. These conditions are very general since they do not depend o ..."
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We characterize the Gneiting class of space–time covariance functions and give more relaxed conditions on the functions involved. We then show necessary conditions for the construction of compactly supported functions of the Gneiting type. These conditions are very general since they do not depend on the Euclidean norm.
On an iteration leading to a qanalogue of the Digamma
, 2012
"... We show that the qDigamma function ψq for 0 < q < 1 appears in an iteration studied by Berg and Durán. This is connected with the determination of the probability measure νq on the unit interval with moments 1 / ∑ n+1 k=1 (1 − q)/(1 − qk), which are qanalogues of the reciprocals of the harm ..."
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We show that the qDigamma function ψq for 0 < q < 1 appears in an iteration studied by Berg and Durán. This is connected with the determination of the probability measure νq on the unit interval with moments 1 / ∑ n+1 k=1 (1 − q)/(1 − qk), which are qanalogues of the reciprocals of the harmonic numbers. The Mellin transform of the measure νq can be expressed in terms of the qDigamma function. It is shown that νq has a continuous density on]0,1], which is piecewise C ∞ with kinks at the powers of q. Furthermore, (1 − q)e −x νq(e −x) is a standard pfunction from the theory of regenerative phenomena.