Stieltjes fraction
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1: 3.10 Continued Fractions
Stieltjes Fractions
… ►is called a Stieltjes fraction (-fraction). … ►For the same function , the convergent of the Jacobi fraction (3.10.11) equals the convergent of the Stieltjes fraction (3.10.6). …2: Bibliography C
3: Bibliography K
4: Bibliography J
5: 2.6 Distributional Methods
§2.6(ii) Stieltjes Transform
… ►The Stieltjes transform of is defined by … ►Corresponding results for the generalized Stieltjes transform …An application has been given by López (2000) to derive asymptotic expansions of standard symmetric elliptic integrals, complete with error bounds; see §19.27(vi). ►§2.6(iii) Fractional Integrals
…6: 18.40 Methods of Computation
7: Bibliography M
8: Bibliography W
9: Bibliography H
10: Errata
A number of changes were made with regard to fractional integrals and derivatives. In §1.15(vi) a reference to Miller and Ross (1993) was added, the fractional integral operator of order was more precisely identified as the Riemann-Liouville fractional integral operator of order , and a paragraph was added below (1.15.50) to generalize (1.15.47). In §1.15(vii) the sentence defining the fractional derivative was clarified. In §2.6(iii) the identification of the Riemann-Liouville fractional integral operator was made consistent with §1.15(vi).
A new Subsection Continued Fractions, has been added to cover computation of confluent hypergeometric functions by continued fractions.
A new Subsection Continued Fractions, has been added to cover computation of the Gauss hypergeometric functions by continued fractions.