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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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Cited by 10 (8 self)
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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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Cited by 3 (0 self)
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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.
A Systematic List of Two and Threeterm Contiguous Relations for Basic Hypergeometric Series
"... ..."
On the Theory of the Γq Function
, 2009
"... We consider the Γq function for 0 < q  < 1 and complex function values. qAnalogues of Euler’s constant, the Gaussian Ψ function, the Euler and Weierstrass formulas for Γ(z) are introduced. The meromorphic continuation of the Γqfunction is found. For the qRiemann zeta function [26], we show a mul ..."
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We consider the Γq function for 0 < q  < 1 and complex function values. qAnalogues of Euler’s constant, the Gaussian Ψ function, the Euler and Weierstrass formulas for Γ(z) are introduced. The meromorphic continuation of the Γqfunction is found. For the qRiemann zeta function [26], we show a multiplication formula with the Γq function. The Jacobi elliptic functions sn u, cn u and dn u may be expressed in the form sin x, cosx and 1 times a balanced Γq function. We give a solution of the Truesdell [40] Fq equation.
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 harmonic n ..."
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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.