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91
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 19 (7 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.
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 set of ..."
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Cited by 18 (8 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.
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.
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 6 (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...
Generalized hypergeometric functions at unit argument
 Proc. Amer. Math. Soc
, 1992
"... Abstract. The analytic continuation near z = 1 of the hypergeometric function p+xFp(z) is obtained for arbitrary p = 2,3,..., including the exceptional cases when the sum of the denominator parameters minus the sum of the numerator parameters is equal to an integer. 1. ..."
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Cited by 5 (2 self)
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Abstract. The analytic continuation near z = 1 of the hypergeometric function p+xFp(z) is obtained for arbitrary p = 2,3,..., including the exceptional cases when the sum of the denominator parameters minus the sum of the numerator parameters is equal to an integer. 1.
Summations for Basic Hypergeometric Series Involving a QAnalogue of the Digamma Function
, 1996
"... Using a simple method, numerous summation formulas for hypergeometric and basic hypergeometric series are derived. Among these summation formulas are nonterminating extensions and qextensions of identities recorded by Lavoie, Luke, Watson, and Srivastava. At the result side of the basic hypergeomet ..."
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Cited by 5 (1 self)
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Using a simple method, numerous summation formulas for hypergeometric and basic hypergeometric series are derived. Among these summation formulas are nonterminating extensions and qextensions of identities recorded by Lavoie, Luke, Watson, and Srivastava. At the result side of the basic hypergeometric summations there appears a qanalogue of the digamma function. Some of its properties are also studied. 1.
A random tiling model for two dimensional electrostatics
 Mem. Amer. Math. Soc
"... Abstract. We consider triangular holes on the hexagonal lattice and we study their interaction when the rest of the lattice is covered by dimers. More precisely, we analyze the joint correlation of these triangular plurimers in a “sea ” of dimers. We determine the asymptotics of the joint correlatio ..."
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Cited by 5 (5 self)
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Abstract. We consider triangular holes on the hexagonal lattice and we study their interaction when the rest of the lattice is covered by dimers. More precisely, we analyze the joint correlation of these triangular plurimers in a “sea ” of dimers. We determine the asymptotics of the joint correlation (for large separations between the holes) in the case when one of the plurimers has odd side length, all remaining plurimers have evenlength sides, and the plurimers are distributed symmetrically with respect to a symmetry axis. Our result has a striking physical interpretation. If we regard the plurimers as electrical charges, with charge equal to the difference between the number of downpointing and uppointing unit triangles in a plurimer, the logarithm of the joint correlation behaves exactly like the electrostatic potential energy of this twodimensional electrostatic system: it is obtained by a Superposition Principle from the interaction of all pairs, and the pair interactions are according to Coulomb’s law. As far as the author knows, there are no results in the literature similar to the Superposition Principle presented in this paper. 1.
Toward verification of the Riemann hypothesis: Application of the Li criterion, to appear in
 Math. Phys., Analysis and Geometry (2005). 14 M. W. Coffey, New
, 2004
"... We substantially apply the Li criterion for the Riemann hypothesis to hold. Based upon a series representation for the sequence {λk}, which are certain logarithmic derivatives of the Riemann xi function evaluated at unity, we determine new bounds for relevant Riemann zeta function sums and the seque ..."
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Cited by 4 (2 self)
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We substantially apply the Li criterion for the Riemann hypothesis to hold. Based upon a series representation for the sequence {λk}, which are certain logarithmic derivatives of the Riemann xi function evaluated at unity, we determine new bounds for relevant Riemann zeta function sums and the sequence itself. We find that the Riemann hypothesis holds if certain conjectured properties of a sequence ηj are valid. The constants ηj enter the Laurent expansion of the logarithmic derivative of the zeta function about s = 1 and appear to have remarkable characteristics. On our conjecture, not only does the Riemann hypothesis follow, but an inequality governing the values λn and inequalities for the sums of reciprocal powers of the nontrivial zeros of the zeta function. Key words and phrases Riemann zeta function, Riemann xi function, logarithmic derivatives, Riemann hypothesis,