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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 ..."
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Cited by 21 (1 self)
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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.
Joint Iterative Decoding of LDPC Codes and Channels with Memory
, 2003
"... This paper considers the joint iterative decoding of irregular lowdensity paritycheck (LDPC) codes and channels with memory. It begins by introducing a new class of erasure channels with memory, known as generalizederasure channels. For these channels, a single parameter recursion for the density ..."
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Cited by 8 (5 self)
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This paper considers the joint iterative decoding of irregular lowdensity paritycheck (LDPC) codes and channels with memory. It begins by introducing a new class of erasure channels with memory, known as generalizederasure channels. For these channels, a single parameter recursion for the density evolution of the joint iterative decoder is derived. This provides a necessary and sucient condition for decoder convergence, and allows the algebraic construction of sequences of LDPC degree distributions. Under certain conditions, these sequences can achieve the symmetric information rate (SIR) of the channel using only iterative decoding. Example code sequences are given for two channels, and it is conjectured that they each achieve the respective SIR. Keywords: joint iterative decoding, erasure channel, capacityachieving, LDPC codes 1.
Complete monotonicity of some functions involving polygamma functions, submitted
"... Abstract. In the present paper, we establish necessary and sufficient conditions for the functions x α ˛ ˛ψ (i) (x + β) ˛ ˛ and α ˛ ˛ψ (i) (x + β) ˛ ˛ − x ˛ ˛ψ (i+1) (x + β) ˛ ˛ respectively to be monotonic and completely monotonic on (0, ∞), where i ∈ N, α> 0 and β ≥ 0 are scalars, and ψ ( ..."
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Cited by 3 (3 self)
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Abstract. In the present paper, we establish necessary and sufficient conditions for the functions x α ˛ ˛ψ (i) (x + β) ˛ ˛ and α ˛ ˛ψ (i) (x + β) ˛ ˛ − x ˛ ˛ψ (i+1) (x + β) ˛ ˛ respectively to be monotonic and completely monotonic on (0, ∞), where i ∈ N, α> 0 and β ≥ 0 are scalars, and ψ (i) (x) are polygamma functions. 1.
DERIVATION OF INDEX THEOREM BY SUPERSYMMETRY
, 804
"... Abstract. In order to evaluate some quantities in Gaussian ensembles, we investigate ”vandermonde ensemble ” which represents the distribution of eigenvalues of GUE in the phase space. We derive the integral equation of the level density of vandermonde ensemble and we compute the level density numer ..."
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Abstract. In order to evaluate some quantities in Gaussian ensembles, we investigate ”vandermonde ensemble ” which represents the distribution of eigenvalues of GUE in the phase space. We derive the integral equation of the level density of vandermonde ensemble and we compute the level density numerically. 1.
A NEW PROOF OF SEMICIRCLE LAW OF FIXED TRACE SQUARE ENSEMBLE
, 804
"... Abstract. In the present paper, we give a simple proof of the level density of fixed trace square ensemble. We derive the integral equation of the level density of fixed trace square ensemble.Then we analyze the asymptotic behavior of the level density. 1. ..."
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Abstract. In the present paper, we give a simple proof of the level density of fixed trace square ensemble. We derive the integral equation of the level density of fixed trace square ensemble.Then we analyze the asymptotic behavior of the level density. 1.
MSC: Primary 33B15; Secondary 41A60
, 2009
"... Completely monotonic functions of positive order and asymptotic expansions of the logarithm of Barnes double gamma function and Euler’s gamma function ..."
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Completely monotonic functions of positive order and asymptotic expansions of the logarithm of Barnes double gamma function and Euler’s gamma function
AN ASYMPTOTIC EXPANSION FOR THE INCOMPLETE BETA FUNCTION
"... Abstract. A new asymptotic expansion is derived for the incomplete beta function I(a, b, x), which is suitable for large a, smallband x>0.5. This expansion is of the form I(a, b, x) ∼ Q(b, −γ log x)+ Γ(a + b) Γ(a)Γ(b) xγ Tn(b, x)/γ n+1, where Q is the incomplete Gamma function ratio and γ = a+(b ..."
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Abstract. A new asymptotic expansion is derived for the incomplete beta function I(a, b, x), which is suitable for large a, smallband x>0.5. This expansion is of the form I(a, b, x) ∼ Q(b, −γ log x)+ Γ(a + b) Γ(a)Γ(b) xγ Tn(b, x)/γ n+1, where Q is the incomplete Gamma function ratio and γ = a+(b−1)/2.This form has some advantages over previous asymptotic expansions in this region in which Tn depends on a as well as on b and x.