1—10 of 91 matching pages
A new lower bound in the second Kershaw’s double inequality.
J. Comput. Appl. Math. 214 (2), pp. 610–616.
Uniform asymptotic expansions of a double integral: Coalescence of two stationary points.
Proc. Roy. Soc. London Ser. A 456, pp. 407–431.
3: Gerhard Wolf
… ► Schmidt) of the Chapter Double Confluent Heun Equation in the book Heun’s Differential Equations (A. …
… ►If has a double zero , or more generally is a zero of order , , then uniform asymptotic approximations (but not expansions) can be constructed in terms of Bessel functions, or modified Bessel functions, of order . The number can also be replaced by any real constant in the sense that is analytic and nonvanishing at ; moreover, is permitted to have a single or double pole at . The order of the approximating Bessel functions, or modified Bessel functions, is , except in the case when has a double pole at . … ►
§10.72(iii) Differential Equations with a Double Pole and a Movable Turning Point►In (10.72.1) assume and depend continuously on a real parameter , has a simple zero and a double pole , except for a critical value , where . …
31.9.2… ►The integration path is called a Pochhammer double-loop contour (compare Figure 5.12.3). … ►
§31.9(ii) Double Orthogonality… ►and the integration paths , are Pochhammer double-loop contours encircling distinct pairs of singularities , , . …
9: 8.13 Zeros
… ►As increases the positive zeros coalesce to form a double zero at (). The values of the first six double zeros are given to 5D in Table 8.13.1. … ►
… ►Other methods include numerical quadrature applied to double and multiple integral representations. …