Barycentric form of Lagrange interpolation

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11: 1.10 Functions of a Complex Variable

… ►A cut neighborhood is formed by deleting a ray emanating from the center. … ►

Lagrange Inversion Theorem

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Extended Inversion Theorem

… ►It should be noted that different branches of ${(w-w_0)}^{1/\mu }$ used in forming ${(w-w_0)}^{n/\mu }$ in (1.10.16) give rise to different solutions of (1.10.12). … ►Let $F(x,z)$ have a converging power series expansion of the form …

12: 33.18 Limiting Forms for Large $\mathrm{\ell }$

§33.18 Limiting Forms for Large $\mathrm{\ell }$

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13: 3.8 Nonlinear Equations

… ►Sometimes the equation takes the form … ►

Regula Falsi

… ►Inverse linear interpolation (§3.3(v)) is used to obtain the first approximation: …

14: 2.2 Transcendental Equations

… ►where $F_0=f_0$ and $s{F}_s$ ($s\ge 1$) is the coefficient of $x^{-1}$ in the asymptotic expansion of ${(f(x))}^s$ (Lagrange’s formula for the reversion of series). …

15: Bibliography T

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Laplace type integrals: Transformation to standard form and uniform asymptotic expansions. Quart. Appl. Math. 43 (1), pp. 103–123.

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External Links:

ISSN 0033-569X, FullText, MathReview (I. Fenyő), ZentralBlatt

Referenced by:

§2.4(i).

Encodings:

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Six myths of polynomial interpolation and quadrature. Math. Today (Southend-on-Sea) 47 (4), pp. 184–188.

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External Links:

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Referenced by:

§3.5(iv), §3.5(iv), Ch.3.

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Algebraic transformations of hypergeometric functions and automorphic forms on Shimura curves. Trans. Amer. Math. Soc. 365 (12), pp. 6697–6729.

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External Links:

ISSN 0002-9947, Document, FullText, MathReview (John M. Voight), ZentralBlatt

Referenced by:

§15.8(v), §15.8(v).

Encodings:

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16: 31.12 Confluent Forms of Heun’s Equation

§31.12 Confluent Forms of Heun’s Equation

►Confluent forms of Heun’s differential equation (31.2.1) arise when two or more of the regular singularities merge to form an irregular singularity. …There are four standard forms, as follows: … ►This has regular singularities at $z=0$ and $1$, and an irregular singularity of rank 1 at $z=\mathrm{\infty }$. … ►

17: Bibliography L

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Reduction of Elliptic Integrals to Legendre Normal Form. Technical report Technical Report 97-21, Department of Computer Science, University of Waterloo, Waterloo, Ontario.

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Referenced by:

§19.14(ii).

Encodings:

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Démonstration d’un Théoréme d’Arithmétique. Nouveau Mém. Acad. Roy. Sci. Berlin, pp. 123–133 (French).

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Notes:

Reprinted in Oeuvres, Vol. 3, pp. 189–201, Gauthier-Villars, Paris, 1867

External Links:

FullText

Referenced by:

§27.13(iii).

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Adjusted forms of the Fourier coefficient asymptotic expansion and applications in numerical quadrature. Math. Comp. 25 (113), pp. 87–104.

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External Links:

FullText, MathReview (J. Bryant), ZentralBlatt

Referenced by:

§2.3(iv).

Encodings:

BibTeX

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18: Frank Garvan

… ►His research is in the areas of $q$-series and modular forms, and he enjoys using MAPLE in his research. …

19: 3.11 Approximation Techniques

… ►If $J=n+1$, then $p_n(x)$ is the Lagrange interpolation polynomial for the set $x_1,x_2,\mathrm{\dots },x_J$ (§3.3(i)). … ►For many applications a spline function is a more adaptable approximating tool than the Lagrange interpolation polynomial involving a comparable number of parameters; see §3.3(i), where a single polynomial is used for interpolating $f(x)$ on the complete interval $[a,b]$. …

20: Annie A. M. Cuyt

… ►A lot of her research has been devoted to rational approximations, in one as well as in many variables, and sparse interpolation. …