1—10 of 148 matching pages
Integrals with a large parameter. Several nearly coincident saddle-points.
Proc. Cambridge Philos. Soc. 72, pp. 49–65.
Integrals with a large parameter: A double complex integral with four nearly coincident saddle-points.
Math. Proc. Cambridge Philos. Soc. 87 (2), pp. 249–273.
Integrals with a large parameter: Legendre functions of large degree and fixed order.
Math. Proc. Cambridge Philos. Soc. 95 (2), pp. 367–380.
2: Karl Dilcher
… ►Over the years he authored or coauthored numerous papers on Bernoulli numbers and related topics, and he maintains a large on-line bibliography on the subject. …
… ►If , then as with , … ►If , then as with , … ►If , then as with , … ►For other extensions, see Wagner (1986), Temme (2003) and Temme (2015, Chapters 12 and 28).
4: 10.70 Zeros
… ►If is a large positive integer, then …
5: 13.9 Zeros
… ►where is a large positive integer, and the logarithm takes its principal value (§4.2(i)). … ►For fixed and in the large -zeros of are given by …where is a large positive integer. … ►For fixed and in the large -zeros of are given by …where is a large positive integer. …
§8.11(i) Large , Fixed… ►
§8.11(ii) Large , Fixed… ►
§8.11(iii) Large , Fixed… ►
§8.11(iv) Large , Bounded…
… ►These products resulted from the leadership of the Editors and Associate Editors pictured in Figure 1; the contributions of 29 authors, 10 validators, and 5 principal developers; and assistance from a large group of contributing developers, consultants, assistants and interns. …
§13.8(i) Large , Fixed and… ►When the foregoing results are combined with Kummer’s transformation (13.2.39), an approximation is obtained for the case when is large, and and are bounded. ►
§13.8(ii) Large and , Fixed and… ►
§13.8(iii) Large… ► …
… ►Large values of or , for example, delay convergence of the Gauss series, and may also lead to severe cancellation. … ►Initial values for moderate values of and can be obtained by the methods of §15.19(i), and for large values of , , or via the asymptotic expansions of §§15.12(ii) and 15.12(iii). ►For example, in the half-plane we can use (15.12.2) or (15.12.3) to compute and , where is a large positive integer, and then apply (15.5.18) in the backward direction. …
… ►where is a real or complex variable and is a large real or complex parameter. … ►In regions in which (10.72.1) has a simple turning point , that is, and are analytic (or with weaker conditions if is a real variable) and is a simple zero of , asymptotic expansions of the solutions for large can be constructed in terms of Airy functions or equivalently Bessel functions or modified Bessel functions of order (§9.6(i)). … ►In regions in which the function has a simple pole at and is analytic at (the case in §10.72(i)), asymptotic expansions of the solutions of (10.72.1) for large can be constructed in terms of Bessel functions and modified Bessel functions of order , where is the limiting value of as . …