# for sequences

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## 1—10 of 43 matching pages

##### 1: 3.9 Acceleration of Convergence
###### §3.9(i) Sequence Transformations
All sequences (series) in this section are sequences (series) of real or complex numbers. … , a sequence for which …
###### §3.9(iv) Shanks’ Transformation
Sequences that are accelerated by Levin’s transformation include logarithmically convergent sequences, i. …
##### 2: 3.12 Mathematical Constants
3.12.1 $\pi=3.14159\;26535\;89793\;23846\;\ldots$
3.12.3 $e=2.71828\;18284\;59045\;23536\;\ldots\,,$
3.12.4 $\gamma=0.57721\;56649\;01532\;86060\;\ldots,$
##### 3: 1.17 Integral and Series Representations of the Dirac Delta
###### §1.17(i) Delta Sequences
for a suitably chosen sequence of functions $\delta_{n}\left(x\right)$, $n=1,2,\dots$. Such a sequence is called a delta sequence and we write, symbolically,
1.17.4 $\lim_{n\to\infty}\delta_{n}\left(x\right)=\delta\left(x\right),$ $x\in\mathbb{R}$.
An example of a delta sequence is provided by …
##### 4: 26.22 Software
• On-Line Encyclopedia of Integer Sequences (website).

• ##### 5: 3.6 Linear Difference Equations
Many special functions satisfy second-order recurrence relations, or difference equations, of the form …
3.6.4 $w_{n}/g_{n}\to 0,$ $n\to\infty$.
At the same time we construct a sequence $e_{n}$, $n=0,1,\dots$, defined by
3.6.8 $a_{n}e_{n}=c_{n}e_{n-1}-d_{n}p_{n},$
3.6.10 $p_{n+1}w_{n}=p_{n}w_{n+1}+e_{n},$
##### 7: 2.1 Definitions and Elementary Properties
Let $\phi_{s}(x)$, $s=0,1,2,\dots$, be a sequence of functions defined in $\mathbf{X}$ such that for each $s$
2.1.19 $\phi_{s+1}(x)=o\left(\phi_{s}(x)\right),$ $x\to c$ in $\mathbf{X}$,
Then $\{\phi_{s}(x)\}$ is an asymptotic sequence or scale. Suppose also that $f(x)$ and $f_{s}(x)$ satisfy
2.1.20 $f(x)=\sum_{s=0}^{n-1}f_{s}(x)+O\left(\phi_{n}(x)\right),$ $x\to c$ in $\mathbf{X}$,
##### 8: 1.9 Calculus of a Complex Variable
###### §1.9(v) Infinite Sequences and Series
This sequence converges pointwise to a function $f(z)$ if …
##### 9: 3.8 Nonlinear Equations
Let $z_{1},z_{2},\dots$ be a sequence of approximations to a root, or fixed point, $\zeta$. …for all $n$ sufficiently large, where $A$ and $p$ are independent of $n$, then the sequence is said to have convergence of the $p$th order. … For real functions $f(x)$ the sequence of approximations to a real zero $\xi$ will always converge (and converge quadratically) if either: … Starting this iteration in the neighborhood of one of the four zeros $\pm 1,\pm\mathrm{i}$, sequences $\{z_{n}\}$ are generated that converge to these zeros. For an arbitrary starting point $z_{0}\in\mathbb{C}$, convergence cannot be predicted, and the boundary of the set of points $z_{0}$ that generate a sequence converging to a particular zero has a very complicated structure. …
##### 10: Guide to Searching the DLMF
• phrase:

any double-quoted sequence of textual words and numbers.

• math expression:

any -like sequence of terms, excluding phrases.

• If you do not want a term or a sequence of terms in your query to undergo math processing, you should quote them as a phrase. …