Error Bounds for the Asymptotic Expansion of the Ratio of Two Gamma Functions with Complex Argument

1992 ◽  
Vol 23 (2) ◽  
pp. 505-511 ◽  
Author(s):  
C. L. Frenzen
Keyword(s):  
Asymptotic Expansion ◽  
Error Bounds ◽  
Gamma Functions ◽  
Complex Argument

scholarly journals An asymptotic expansion for a ratio of products of gamma functions

2000 ◽  
Vol 24 (8) ◽  
pp. 505-510 ◽  
Author(s):  
Wolfgang Bühring
Keyword(s):  
Asymptotic Expansion ◽  
Gamma Functions

An asymptotic expansion of a ratio of products of gamma functions is derived. It generalizes a formula which was stated by Dingle, first proved by Paris, and recently reconsidered by Olver

Corrigendum and addendum to ‘asymptotic series for double zeta, double gamma and Hecke L-functions’

2002 ◽  
Vol 132 (2) ◽  
pp. 377-384 ◽  
Author(s):  
KOHJI MATSUMOTO
Keyword(s):  
Asymptotic Expansion ◽  
Asymptotic Series ◽  
Gamma Functions ◽  
Double Zeta ◽  
Error Terms

Refined expressions are given for the error terms in the asymptotic expansion formulas for double zeta and double gamma functions, proved in the author's former paper [2]. Some inaccurate claims in [2] are corrected.

scholarly journals Error bounds for the asymptotic expansion of the Hurwitz zeta function

2017 ◽  
Vol 473 (2203) ◽  
pp. 20170363 ◽  
Author(s):  
G. Nemes
Keyword(s):  
Asymptotic Expansion ◽  
Zeta Function ◽  
Gamma Function ◽  
Error Bounds ◽  
Asymptotic Expansions ◽  
Remainder Term ◽  
Hurwitz Zeta Function ◽  
Polygamma Functions

In this paper, we reconsider the large- a asymptotic expansion of the Hurwitz zeta function ζ ( s , a ). New representations for the remainder term of the asymptotic expansion are found and used to obtain sharp and realistic error bounds. Applications to the asymptotic expansions of the polygamma functions, the gamma function, the Barnes G -function and the s -derivative of the Hurwitz zeta function ζ ( s , a ) are provided. A detailed discussion on the sharpness of our error bounds is also given.

A Uniform Asymptotic Expansion of the Jacobi Polynomials with Error Bounds

1985 ◽  
Vol 37 (5) ◽  
pp. 979-1007 ◽  
Author(s):  
C. L. Frenzen ◽  
R. Wong
Keyword(s):  
Asymptotic Behavior ◽  
Asymptotic Expansion ◽  
Error Bounds ◽  
Jacobi Polynomials ◽  
Lebesgue Constants ◽  
Uniform Asymptotic Expansion ◽  
Leading Term ◽  
Image Position

In a recent investigation of the asymptotic behavior of the Lebesgue constants for Jacobi polynomials, we encountered the problem of obtaining an asymptotic expansion for the Jacobi polynomials , as n → ∞, which is uniformly valid for θ in . The leading term of such an expansion is provided by the following well-known formula of “Hilb's type” [13, p. 197]:(1.1)where α > – 1, β real and ; c and are fixed positive numbers. Note that the remainder in (1.1) is always θ1/2O(n–3/2).

scholarly journals THE GENERALIZED GOODWIN–STATON INTEGRAL

2005 ◽  
Vol 48 (3) ◽  
pp. 635-650 ◽  
Author(s):  
D. S. Jones
Keyword(s):  
Asymptotic Expansion ◽  
Error Bounds ◽  
Oscillatory Case

AbstractSome properties of the generalized Goodwin–Staton integral are derived. Explicit error bounds for the asymptotic expansion are determined. In addition, results are obtained for the oscillatory case and when logarithmic factors are present.

Sign in / Sign up

Export Citation Format

Share Document