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Convenient for immediate computer implementation equivalents of Green’s functions are obtained for boundary-contact value problems posed for two-dimensional Laplace and Klein-Gordon equations on some regions filled in with piecewise homogeneous isotropic conductive materials. Dirichlet, Neumann and Robin conditions are allowed on the outer boundary of a simply-connected region, while conditions of ideal contact are assumed on interface lines. The objective in this study is to widen the range of...

Efficient Stable Ways to Calculate Continued Fraction Coefficients From some Series.

A.N. Stokes (1983)

Numerische Mathematik

Evaluation of coefficients of a double Chebyshev series of the function g(p(x+y))

Krystyna Ziętak (1988)

Applicationes Mathematicae

Fast multilevel evaluation of smooth radial basis function expansions.

Livne, Oren E., Wright, Grady B. (2006)

ETNA. Electronic Transactions on Numerical Analysis [electronic only]

Forme confluente de l'e-algorithme topologique.

C. Brezinski (1974/1975)

Numerische Mathematik

Formulas for sums of powers of integers by functional equations.

Donald R. Snow (1978)

Aequationes mathematicae

Nilakantha's accelerated series for π

David Brink (2015)

Acta Arithmetica

We show how the idea behind a formula for π discovered by the Indian mathematician and astronomer Nilakantha (1445-1545) can be developed into a general series acceleration technique which, when applied to the Gregory-Leibniz series, gives the formula $π = \sum_{n = 0}^{\infty} ((5 n + 3) n! (2 n)!) / (2^{n - 1} (3 n + 2)!)$ with convergence as $13 . 5^{- n}$ , in much the same way as the Euler transformation gives $π = \sum_{n = 0}^{\infty} (2^{n + 1} n! n!) / (2 n + 1)!$ with convergence as $2^{- n}$ . Similar transformations lead to other accelerated series for π, including three “BBP-like” formulas, all of which are collected in the Appendix....

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