Results 1  10
of
159
The Askeyscheme of hypergeometric orthogonal polynomials and its qanalogue
, 1998
"... We list the socalled Askeyscheme of hypergeometric orthogonal polynomials and we give a q analogue of this scheme containing basic hypergeometric orthogonal polynomials. In chapter 1 we give the definition, the orthogonality relation, the three term recurrence relation, the second order di#erent ..."
Abstract

Cited by 581 (6 self)
 Add to MetaCart
We list the socalled Askeyscheme of hypergeometric orthogonal polynomials and we give a q analogue of this scheme containing basic hypergeometric orthogonal polynomials. In chapter 1 we give the definition, the orthogonality relation, the three term recurrence relation, the second order di#erential or di#erence equation, the forward and backward shift operator, the Rodriguestype formula and generating functions of all classes of orthogonal polynomials in this scheme. In chapter 2 we give the limit relations between di#erent classes of orthogonal polynomials listed in the Askeyscheme. In chapter 3 we list the qanalogues of the polynomials in the Askeyscheme. We give their definition, orthogonality relation, three term recurrence relation, second order di#erence equation, forward and backward shift operator, Rodriguestype formula and generating functions. In chapter 4 we give the limit relations between those basic hypergeometric orthogonal polynomials. Finally, in chapter 5 we...
Adaptive Modulation over Nakagami Fading Channels
, 1998
"... We first study the capacity of Nakagami multipath fading (NMF) channels with an average power constraint for three power and rate adaptation policies. We obtain closedform solutions for NMF channel capacity for each power and rate adaptation strategy. Results show that rate adaptation is the key to ..."
Abstract

Cited by 145 (17 self)
 Add to MetaCart
We first study the capacity of Nakagami multipath fading (NMF) channels with an average power constraint for three power and rate adaptation policies. We obtain closedform solutions for NMF channel capacity for each power and rate adaptation strategy. Results show that rate adaptation is the key to increasing link spectral efficiency. We analyze therefore the performance of constantpower variablerate MQAM schemes over NMF channels. We obtain closedform expressions for the outage probability, spectral efficiency and average biterrorrate (BER) assuming perfect channel estimation and negligible time delay. We also analyze the impact of time delay on the BER of adaptive MQAM. Keywords Link Spectral Efficiency, Adaptive Modulation Techniques, and Nakagami Fading. I. Introduction The radio spectrum available for wireless services is extremely scarce, while demand for these services is growing at a rapid pace [1]. Hence spectral efficiency is of primary concern in the design of fut...
Orthogonal polynomials for exponential weights x2ρe−2Q(x) on [0,d
 J. Approx. Theory
"... xi + 476 pp With each of a large class of positive measures µ on the real line it is possible to associate a sequence {pn(x)} of orthogonal polynomials with the property that pm(x)pn(x)dµ(x) = 0, m ̸ = n, 1, m = n. (1) Such a sequence satisfies a three term recurrence relation xpn(x) = anPn+1(x) + ..."
Abstract

Cited by 66 (17 self)
 Add to MetaCart
xi + 476 pp With each of a large class of positive measures µ on the real line it is possible to associate a sequence {pn(x)} of orthogonal polynomials with the property that pm(x)pn(x)dµ(x) = 0, m ̸ = n, 1, m = n. (1) Such a sequence satisfies a three term recurrence relation xpn(x) = anPn+1(x) + bnPn(x) + an−1Pn−1(x) (2) Conversely, for suitable starting values and coefficient sequences {an}, {bn}, the recurrence relation (2) generates a sequence of polynomials satisfying (1) for some measure µ. The polynomials have their zeros within the interval of support of the measure. Examples date from the 19th century. The Jacobi polynomials P (α,β) n (x) are orthogonal with respect to µ with support [−1, 1], where dµ = (1 − x) α+1 (1 +
Algebraic transformations of Gauss hypergeometric functions, preprint
, 2004
"... The paper classifies algebraic transformations of Gauss hypergeometric functions and pullback transformations between hypergeometric differential equations. This classification recovers the classical transformations of degree 2, 3, 4, 6, and finds other transformations of some special classes of th ..."
Abstract

Cited by 39 (13 self)
 Add to MetaCart
The paper classifies algebraic transformations of Gauss hypergeometric functions and pullback transformations between hypergeometric differential equations. This classification recovers the classical transformations of degree 2, 3, 4, 6, and finds other transformations of some special classes of the Gauss hypergeometric function.
The Components of Content
 Philosophy of Mind: Classical and Contemporary Readings. Oxford and
, 2002
"... and 9 are similar to the old version, but the other sections are quite different. Because the old version has ..."
Abstract

Cited by 34 (6 self)
 Add to MetaCart
(Show Context)
and 9 are similar to the old version, but the other sections are quite different. Because the old version has
Impact of channel prediction on adaptive coded modulation performance in Rayleigh fading
 IEEE Trans. Veh. Technol
, 2004
"... Abstract—Adaptive coded modulation (ACM) is a promising tool for increasing the spectral efficiency of timevarying mobile channels while maintaining a predictable biterror rate (BER). An important restriction in systems with such a transmission scheme is that the transmitter needs to have accurate ..."
Abstract

Cited by 33 (4 self)
 Add to MetaCart
Abstract—Adaptive coded modulation (ACM) is a promising tool for increasing the spectral efficiency of timevarying mobile channels while maintaining a predictable biterror rate (BER). An important restriction in systems with such a transmission scheme is that the transmitter needs to have accurate channelstate information (CSI). Earlier analysis of ACM systems usually assumes that the transmitter has perfect knowledge of the channel or that the CSI is accurate but outdated. In this paper, we investigate the effects of predicting the CSI using a linear fadingenvelope predictor in order to enhance the performance of an ACM system. For the case in which multidimensional trellis codes are used on Rayleighfading channels, we obtain approximative closedform expressions for BER and average spectral efficiency. Numerical examples are given for the case of Jakes correlation profile and maximum a posteriorioptimal predictor coefficients. Index Terms—Adaptive modulation, antenna diversity, channel estimation, fading channels. I.
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 ..."
Abstract

Cited by 27 (1 self)
 Add to MetaCart
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.
Adaptive MQam Modulation over Nakagami Fading Channels
 in IEEE Global Communications Conference
, 1997
"... We study the performance of constantpower variablerate MQAM schemes over Nakagami fading channels. We obtain closedform expressions for the outage probability, spectral efficiency and average biterrorrate (BER) assuming perfect channel estimation and negligible time delay. For a target BER of ..."
Abstract

Cited by 17 (2 self)
 Add to MetaCart
We study the performance of constantpower variablerate MQAM schemes over Nakagami fading channels. We obtain closedform expressions for the outage probability, spectral efficiency and average biterrorrate (BER) assuming perfect channel estimation and negligible time delay. For a target BER of 10 \Gamma3 , the spectral efficiency of adaptive continuous rate MQAM comes within 5 dB of the Shannon capacity limit, and adaptive discrete rate MQAM comes within 6.2 dB of this limit. Nonadaptive BPSK suffers a large spectral efficiency penalty relative to these adaptive techniques. We also analyze the impact of time delay on the BER of adaptive MQAM. Results show that systems with low BER requirements will be more sensitive to time delay, but will still operate satisfactorily if the delay is below a critical value. 1. INTRODUCTION The radio spectrum available for wireless services is extremely scarce, while demand for these services is growing at a rapid pace [1]. Spectral efficien...
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 ..."
Abstract

Cited by 15 (0 self)
 Add to MetaCart
(Show Context)
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.
Closed forms: what they are and why we care
, 2010
"... The term “closed form” is one of those mathematical notions that is commonplace, yet virtually devoid of rigor. And, there is disagreement even on the intuitive side; for example, most everyone would say that π + log 2 is a closed form, but some of us would think that the Euler constant γ is not cl ..."
Abstract

Cited by 15 (7 self)
 Add to MetaCart
(Show Context)
The term “closed form” is one of those mathematical notions that is commonplace, yet virtually devoid of rigor. And, there is disagreement even on the intuitive side; for example, most everyone would say that π + log 2 is a closed form, but some of us would think that the Euler constant γ is not closed. Like others before us, we shall try to supply some missing rigor to the notion of closed forms and also to give examples from modern research where the question of closure looms both important and elusive.