Abel means

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31: DLMF Project News

error generating summary

32: 13.29 Methods of Computation

… ►For

M\left(a,b,z\right)

and

M_{\kappa,\mu}\left(z\right)

this means that in the sector

|\operatorname{ph}z|\leq\pi

we may integrate along outward rays from the origin with initial values obtained from (13.2.2) and (13.14.2). …

33: 28.2 Definitions and Basic Properties

… ►Period

\pi

means that the eigenfunction has the property

w(z+\pi)=w(z)

, whereas antiperiod

\pi

means that

w(z+\pi)=-w(z)

. Even parity means

w(-z)=w(z)

, and odd parity means

w(-z)=-w(z)

. …

34: 30.4 Functions of the First Kind

… ►If

f(x)

is mean-square integrable on

[-1,1]

, then formally …

35: 35.1 Special Notation

… ► ►►►

$a, b$	complex variables.
…
$\left\|\mathbf{X}\right\|$	determinant of $\mathbf{X}$ (except when $m=1$ where it means either determinant or absolute value, depending on the context).
…

…

36: 2.1 Definitions and Elementary Properties

… ►(In other words

=

here really means

\subseteq

.) … ►means that for each

n

, the difference between

f(x)

and the

n

th partial sum on the right-hand side is

O\left((x-c)^{n}\right)

x\to c

\mathbf{X}

. …

37: 1.9 Calculus of a Complex Variable

… ►

Mean Value Property

…

38: 3.11 Approximation Techniques

… ►where

x_{\ell}=\cos\left(\pi\ell/n\right)

and the double prime means that the first and last terms are to be halved. … ►Here the single prime on the summation symbol means that the first term is to be halved. … ►Since

L_{0}=1

L_{n}

is a monotonically increasing function of

n

, and (for example)

L_{1000}=4.07\dots

, this means that in practice the gain in replacing a truncated Chebyshev-series expansion by the corresponding minimax polynomial approximation is hardly worthwhile. …