Results 11 to 20 of about 142 (36)

Stokes phenomenon and matched asymptotic expansions [PDF]

, 1995
This paper describes the use of matched asymptotic expansions to illuminate the description of functions exhibiting Stokes phenomenon. In particular the approach highlights the way in which the local structure and the possibility of finding Stokes ...
A. B. Olde Daalhuis, J. R. King, J. R. Ockendon, Olver F. W. J., Olver F. W. J., Olver Frank W. J., Paris R. B., R. H. Tew, S. J. Chapman, Van Dyke Milton   +9 more
core   +2 more sources

The Asymptotic Expansion of Kummer Functions for Large Values of the $a$-Parameter, and Remarks on a Paper by Olver [PDF]

, 2016
It is shown that a known asymptotic expansion of the Kummer function $U(a,b,z)$ as $a$ tends to infinity is valid for $z$ on the full Riemann surface of the logarithm.
Volkmer, Hans
core   +1 more source

The resurgence properties of the incomplete gamma function I [PDF]

, 2014
In this paper we derive new representations for the incomplete gamma function, exploiting the reformulation of the method of steepest descents by C. J. Howls (Howls, Proc. R. Soc. Lond. A 439 (1992) 373--396).
Nemes, Gergő
core   +3 more sources

A generalisation of an expansion for the Riemann zeta function involving incomplete gamma functions [PDF]

, 2009
We derive an expansion for the Riemann zeta function ζ(s) involving incomplete gamma functions with their second argument proportional to n2p, where n is the summation index and p is a positive integer.
Paris, Richard B.
core   +3 more sources

Some special functions identities arising from commuting operators

, 2008
Commuting is an important property in many cases of investigation of properties of operators as well as in various applications, especially in quantum physics. Using the observation that the generalized weighted differential operator of order $k$ and the
Abramowitz, Bell, Kufner, Mojsej, Mária Hutníková, Ohriska, Ondrej Hutník, Rainville, von Neumann   +8 more
core   +1 more source

Inverse hyperbolic equation, Spectral technique, Regularization method, Operational matrix

Kuwait Journal of Science
Recently, the realm related to Euler's Beta function has played a significant role in the development of special function theory. In this study, a new extension of the special function known as Euler's Beta function with respect to the Mittag-Leffler ...
Firas Ghanim, Hiba Fawzi Al-Janaby, Marwan Al-Momani   +2 more
doaj   +1 more source

A class of completely monotonic functions involving divided differences of the psi and polygamma functions and some applications

, 2009
A class of functions involving the divided differences of the psi function and the polygamma functions and originating from Kershaw's double inequality are proved to be completely monotonic.
Guo, Bai-Ni, Qi, Feng
core   +1 more source

An asymptotic expansion for the error term in the Brent-McMillan algorithm for Euler’s constant [PDF]

, 2019
The Brent-McMillan algorithm is the fastest known procedure for the high-precision computation of Euler’s constant γ and is based on the modified Bessel functions I_0(2x) and K_0(2x). An error estimate for this algorithm relies on the optimally truncated
Paris, R. B.
core   +2 more sources

Integral representations for products of two parabolic cylinder functions with different arguments and orders

, 2015
This paper derives new integral representations for products of two parabolic cylinder functions. In particular, expressions are obtained for D_{nu}(x)D_{mu}(y), with x>0 and y>0, that allow for different orders and arguments in the two parabolic ...
Veestraeten, Dirk
core   +1 more source

Some integral representations and limits for (products of) the parabolic cylinder function

, 2015
Veestraeten [1] recently derived inverse Laplace transforms for Laplace transforms that contain products of two parabolic cylinder functions by exploiting the link between the parabolic cylinder function and the transition density and distribution ...
Veestraeten, Dirk
core   +1 more source