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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 ..."
Abstract
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Cited by 7 (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.
pe xp Γ(m+1) Study of a Class of Regularizations of 1/|x | using Gaussian Integrals
, 1999
"... This paper presents a comprehensive study of the functions V p m(x) = x (tp − x p) m e −tp dt for x> 0, m> −1 and p> 0. For large x these functions approximate x1−p. The case p = 2 is of particular (x) ≈ 1/x can be regarded as importance because the functions V 2 m one-dimensional regularizations o ..."
Abstract
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This paper presents a comprehensive study of the functions V p m(x) = x (tp − x p) m e −tp dt for x> 0, m> −1 and p> 0. For large x these functions approximate x1−p. The case p = 2 is of particular (x) ≈ 1/x can be regarded as importance because the functions V 2 m one-dimensional regularizations of the Coulomb potential 1/|x | which are finite at the origin for m> −1 2.
