1—10 of 16 matching pages
1: 18.13 Continued Fractions
… ► is the denominator of the th approximant to: …and is the denominator of the th approximant to: … ► is the denominator of the th approximant to: … ► is the denominator of the th approximant to: … ► is the denominator of the th approximant to: …
2: 3.11 Approximation Techniques
… ►is called a Padé approximant at zero of if …It is denoted by . Thus if , then the Maclaurin expansion of (3.11.21) agrees with (3.11.20) up to, and including, the term in . … ►The array of Padé approximants …Approximants with the same denominator degree are located in the same column of the table. …
3: 36.13 Kelvin’s Ship-Wave Pattern
4: 3.10 Continued Fractions
5: 8.10 Inequalities
6: 1.12 Continued Fractions
7: 10.72 Mathematical Applications
… ►Bessel functions and modified Bessel functions are often used as approximants in the construction of uniform asymptotic approximations and expansions for solutions of linear second-order differential equations containing a parameter. …
8: 13.31 Approximations
… ►For a discussion of the convergence of the Padé approximants that are related to the continued fraction (13.5.1) see Wimp (1985). …
9: Bibliography W
A rational approximant for the digamma function.
Numer. Algorithms 33 (1-4), pp. 499–507.
Some explicit Padé approximants for the function and a related quadrature formula involving Bessel functions.
SIAM J. Math. Anal. 16 (4), pp. 887–895.
10: 2.4 Contour Integrals
… ►For a coalescing saddle point and a pole see Wong (1989, Chapter 7) and van der Waerden (1951); in this case the uniform approximants are complementary error functions. For a coalescing saddle point and endpoint see Olver (1997b, Chapter 9) and Wong (1989, Chapter 7); if the endpoint is an algebraic singularity then the uniform approximants are parabolic cylinder functions with fixed parameter, and if the endpoint is not a singularity then the uniform approximants are complementary error functions. …