relation to infinite partial fractions
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… ►If , , then the integral is defined analogously to the infinite integrals in §1.4(v). … ►
§1.9(v) Infinite Sequences and Series… ►This sequence converges pointwise to a function if … ► … ►
§1.9(vii) Inversion of Limits…
§1.10(ix) Infinite Products… ►The convergence of the infinite product is uniform if the sequence of partial products converges uniformly. … ►
§1.10(x) Infinite Partial Fractions… ►
§16.7 Relations to Other Functions…
§3.10(ii) Relations to Power Series… ►can be converted into a continued fraction of type (3.10.1), and with the property that the th convergent to is equal to the th partial sum of the series in (3.10.3), that is, … ►
Stieltjes Fractions… ►The and of (3.10.2) can be computed by means of three-term recurrence relations (1.12.5). … ►This forward algorithm achieves efficiency and stability in the computation of the convergents , and is related to the forward series recurrence algorithm. …
§6.11 Relations to Other Functions… ►
Incomplete Gamma Function… ►
Confluent Hypergeometric Function►
Normal limit theorems for symmetric random matrices.
Probab. Theory Related Fields 112 (3), pp. 411–423.
A code to calculate (high order) Bessel functions based on the continued fractions method.
Comput. Phys. Comm. 76 (3), pp. 381–388.
Partial fractions expansions and identities for products of Bessel functions.
J. Math. Phys. 46 (4), pp. 043509–1–043509–18.
The similarity solution for the Korteweg-de Vries equation and the related Painlevé transcendent.
Proc. Roy. Soc. London Ser. A 361, pp. 265–275.
On Simple Waves with Profiles in the form of some Special Functions—Chebyshev-Hermite, Mathieu, Whittaker—in Two-phase Media.
In Differential Operators and Related Topics, Vol. I (Odessa,
Operator Theory: Advances and Applications, Vol. 117, pp. 313–322.
… ►However, by appropriate choice of the constant in (15.15.1) we can obtain an infinite series that converges on a disk containing . Moreover, it is also possible to accelerate convergence by appropriate choice of . … ►