large a or b
1—10 of 563 matching pages
On the equation
Acta Arith. 51 (4), pp. 349–368.
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
… ►Karl Dilcher (b. … ►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. …
… ►For large and with see López and Pagola (2011). … ►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: 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… ►where … ►
§8.11(iv) Large , Bounded…
§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. ►For fast computation of with and complex, and with application to Pöschl–Teller–Ginocchio potential wave functions, see Michel and Stoitsov (2008). … ►The relations in §15.5(ii) can be used to compute , provided that care is taken to apply these relations in a stable manner; see §3.6(ii). 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. …
… ►Asymptotic expansions of for large are given in Luke (1969a, §§5.7 and 5.10) and Luke (1975, §5.9). …
… ►Bickel, B. …Eberhardt, B. … B. … B. …Undoubtedly, the editors have overlooked some individuals who contributed, as is inevitable in a large long-lasting project. …
10: Bibliography F
Algorithms and codes for the Macdonald function: Recent progress and comparisons.
J. Comput. Appl. Math. 161 (1), pp. 179–192.
Uniform asymptotic expansions for hypergeometric functions with large parameters IV.
Anal. Appl. (Singap.) 12 (6), pp. 667–710.
On the reciprocal modulus relation for elliptic integrals.
SIAM J. Math. Anal. 1 (4), pp. 524–526.
Uniform asymptotic expansions of certain classes of Meijer -functions for a large parameter.
SIAM J. Math. Anal. 4 (3), pp. 482–507.
Uniform asymptotic expansions of a class of Meijer -functions for a large parameter.
SIAM J. Math. Anal. 14 (6), pp. 1204–1253.