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135
Arithmetic of linear forms involving odd zeta values
 J. Théor. Nombres Bordeaux
, 2001
"... A general hypergeometric construction of linear forms in (odd) zeta values is presented. The construction allows to recover the records of Rhin and Viola for the irrationality measures of #(2) and #(3), as well as to explain Rivoal's recent result on infiniteness of irrational numbers in the se ..."
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Cited by 22 (9 self)
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A general hypergeometric construction of linear forms in (odd) zeta values is presented. The construction allows to recover the records of Rhin and Viola for the irrationality measures of #(2) and #(3), as well as to explain Rivoal's recent result on infiniteness of irrational numbers in the set of odd zeta values, and to prove that at least one of the four numbers #(5), #(7), #(9), and #(11) is irrational. 2000 Mathematics Subject Classification. Primary 11J72, 11J82; Secondary 33C60.
Inequalities for zerobalanced hypergeometric functions
 Trans. Amer. Math. Soc
, 1995
"... Abstract. The authors study certain monotoneity and convexity properties of the Gaussian hypergeometric function and those of the Euler gamma function. 1. ..."
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Cited by 21 (8 self)
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Abstract. The authors study certain monotoneity and convexity properties of the Gaussian hypergeometric function and those of the Euler gamma function. 1.
Adaptive beamforming with a minimum mutual information criterion
 IEEE Trans. on Audio, Speech and Language Processing
, 2007
"... Abstract — In this work, we consider an acoustic beamforming application where two speakers are simultaneously active. We construct one subbanddomain beamformer in generalized sidelobe canceller (GSC) configuration for each source. In contrast to normal practice, we then jointly optimize the active ..."
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Cited by 15 (13 self)
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Abstract — In this work, we consider an acoustic beamforming application where two speakers are simultaneously active. We construct one subbanddomain beamformer in generalized sidelobe canceller (GSC) configuration for each source. In contrast to normal practice, we then jointly optimize the active weight vectors of both GSCs to obtain two output signals with minimum mutual information (MMI). Assuming that the subband snapshots are Gaussiandistributed, this MMI criterion reduces to the requirement that the crosscorrelation coefficient of the subband outputs of the two GSCs vanishes. We also compare separation performance under the Gaussian assumption with that obtained from several superGaussian probability density functions (pdfs), namely, the Laplace, K0, and Γ pdfs. Our proposed technique provides effective nulling of the undesired source, but without the signal cancellation problems seen in conventional beamforming. Moreover, our technique does not suffer from the source permutation and scaling ambiguities encountered in conventional blind source separation algorithms. We demonstrate the effectiveness of our proposed technique through a series of farfield automatic speech recognition experiments on data from the PASCAL Speech Separation Challenge (SSC). On the SSC development data, the simple delayandsum beamformer achieves a word error rate (WER) of 70.4%. The MMI beamformer under a Gaussian assumption achieves a 55.2 % WER, which is further reduced to 52.0 % with a K0 pdf, whereas the WER for data recorded with a closetalking microphone is 21.6%. Index Terms — microphone arrays, beamforming, speech recognition, source separation I.
The hypergeometric function approach to the connection problem for the classical orthogonal polynomials
, 1998
"... Abstract. Let {Pk} and Qk be any two sequences of classical orthogonal polynomials. Using theorems of the theory of generalized hypergeometric functions, we give closedform expressions as well as recurrence relations for the coefficients an,k in the connection equation ..."
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Cited by 10 (0 self)
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Abstract. Let {Pk} and Qk be any two sequences of classical orthogonal polynomials. Using theorems of the theory of generalized hypergeometric functions, we give closedform expressions as well as recurrence relations for the coefficients an,k in the connection equation
Modified ClebschGordantype expansions for products of discrete hypergeometric polynomials.
, 1997
"... Starting from the secondorder difference hypergeometric equation satisfied by the set of discrete orthogonal polynomials fpn g, we find the analytical expressions of the expansion coefficients of any polynomial r m (x) and of the product r m (x)q j (x) in series of the set fpng. These coefficients ..."
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Cited by 8 (4 self)
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Starting from the secondorder difference hypergeometric equation satisfied by the set of discrete orthogonal polynomials fpn g, we find the analytical expressions of the expansion coefficients of any polynomial r m (x) and of the product r m (x)q j (x) in series of the set fpng. These coefficients are given in terms of the polynomial coefficients of the secondorder difference equations satisfied by the involved discrete hypergeometric polynomials. Here q j (x) denotes an arbitrary discrete hypergeometric polynomial of degree j. The particular cases in which fr m g corresponds to the nonorthogonal families fx m g, the rising factorials or Pochhammer polynomials f(x) m g and the falling factorial or Stirling polynomials fx [m] g are considered in detail. The connection problem between discrete hypergeometric polynomials, which here corresponds to the product case with m = 0, is also studied and its complete solution for all the classical discrete orthogonal hypergeometric (CDOH) p...
The evaluation of integrals of Bessel functions via Gfunction identities
 J. Computational and Applied Math
, 1995
"... A few transformations are presented for reducing certain cases of Meijer’s Gfunction to a Gfunction of lower order. Their applications to the integration of a product of Bessel functions are given. The algorithm has been implemented within Mathematica 3.0. 1 ..."
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Cited by 7 (1 self)
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A few transformations are presented for reducing certain cases of Meijer’s Gfunction to a Gfunction of lower order. Their applications to the integration of a product of Bessel functions are given. The algorithm has been implemented within Mathematica 3.0. 1
The distribution of the product of independent Rayleigh random variables
 IEEE Trans. Antennas Propag
, 2006
"... Abstract—We derive the exact probability density functions (pdf) and distribution functions (cdf) of a product of independent Rayleigh distributed random variables. The case = 1 is the classical Rayleigh distribution, while 2 is theRayleigh distribution that has recently attracted interest in wire ..."
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Abstract—We derive the exact probability density functions (pdf) and distribution functions (cdf) of a product of independent Rayleigh distributed random variables. The case = 1 is the classical Rayleigh distribution, while 2 is theRayleigh distribution that has recently attracted interest in wireless propagation research. The distribution functions are derived by using an inverse Mellin transform technique from statistics, and are given in terms of a special function of mathematical physics, the Meijer Gfunction. Series forms of the distribution function are also provided for = 3, 4, 5. We also derive a computationally simple momentbased estimator for the parameter occurring in the distribution, and evaluate its variance. Index Terms—Fading channels, radio propagation, Rayleigh distributions. I.