strictly%20increasing

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1: 4.12 Generalized Logarithms and Exponentials

… ►and is strictly increasing when $0\le x\le 1$. …It, too, is strictly increasing when $0\le x\le 1$, and …

2: 2.2 Transcendental Equations

… ►Let $f(x)$ be continuous and strictly increasing when and …

3: 1.4 Calculus of One Variable

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§1.4(i) Monotonicity

… ►If the $\le$ sign is replaced by , then $f(x)$ is increasing (also called strictly increasing) on $I$. Similarly for nonincreasing and decreasing (strictly decreasing) functions. Each of the preceding four cases is classified as monotonic; sometimes strictly monotonic is used for the strictly increasing or strictly decreasing cases. …

4: 7.8 Inequalities

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7.8.5 $x\ge 0$.

ⓘ

Symbols:

$𝖬\left(x\right)$: Mills’ ratio and $x$: real variable

Referenced by:

§7.8

Permalink:

http://dlmf.nist.gov/7.8.E5

Encodings:

pMML, png, TeX

See also:

Annotations for §7.8 and Ch.7

… ►The function $F\left(x\right)/\sqrt{1-{\mathrm{e}}^{-2x^2}}$ is strictly decreasing for $x>0$. …

5: 18.16 Zeros

… ►Then ${\theta }_{n,m}$ is strictly increasing in $\alpha$ and strictly decreasing in $\beta$; furthermore, if $\alpha =\beta$, then ${\theta }_{n,m}$ is strictly increasing in $\alpha$. …

6: 27.15 Chinese Remainder Theorem

… ►This theorem is employed to increase efficiency in calculating with large numbers by making use of smaller numbers in most of the calculation. …Their product $m$ has 20 digits, twice the number of digits in the data. …These numbers, in turn, are combined by the Chinese remainder theorem to obtain the final result $(modm)$, which is correct to 20 digits. …

7: 26.9 Integer Partitions: Restricted Number and Part Size

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Table 26.9.1: Partitions $p_k\left(n\right)$.

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$n$	$k$
	…
8	0	1	5	10	15	18	20	21	22	22	22
…

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… ►equivalently, partitions into at most $k$ parts either have exactly $k$ parts, in which case we can subtract one from each part, or they have strictly fewer than $k$ parts. …

8: Notices

… ►Reproduction, copying, or distribution for any commercial purpose is strictly prohibited. …

9: 20 Theta Functions

Chapter 20 Theta Functions

…

10: 26.12 Plane Partitions

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Table 26.12.1: Plane partitions.

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$n$	$\mathrm{pp}\left(n\right)$	$n$	$\mathrm{pp}\left(n\right)$	$n$	$\mathrm{pp}\left(n\right)$
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3	6	20	75278	37	903 79784
…

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… ►A descending plane partition is a strict shifted plane partition in which the number of parts in each row is strictly less than the largest part in that row and is greater than or equal to the largest part in the next row. …