Simple Search

Query:

Enter a query and click »Search«...

Format:

Display: entries per page entries

Zbl 1054.65023
Gil, Amparo; Segura, Javier; Temme, Nico M.
Integral representations for computing real parabolic cylinder functions. (English)
[J] Numer. Math. 98, No. 1, 105-134 (2004). ISSN 0029-599X; ISSN 0945-3245/e

Summary: Integral representations are derived for the parabolic cylinder functions $U(a,x)$, $V(a,x)$ and $W(a,x)$ and their derivatives. The new integrals will be used in numerical algorithms based on quadrature. They follow from contour integrals in the complex plane, by using methods from asymptotic analysis (saddle point and steepest descent methods), and are stable starting points for evaluating the functions $U(a,x)$, $V(a,x)$ and $W(a,x)$ and their derivatives by quadrature rules. In particular, the new representations can be used for large parameter cases. Relations of the integral representations with uniform asymptotic expansions are also given. The algorithms will be given in a future paper.

MSC 2000:: *65D20 Computation of special functions
33C10 Cylinder functions, etc.
33F05 Numerical approximation of special functions

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Simple Search

Zentralblatt MATH Berlin [Germany]