DLMF:10.17.E15 (Q3184): Difference between revisions

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		Property / Symbols used
			Q11426
		Property / Symbols used: Q11426 / rank
			Normal rank
		Property / Symbols used: Q11426 / qualifier
			Defining formula: ${\displaystyle{\displaystyle z}}$ z
		Property / Symbols used: Q11426 / qualifier
			xml-id: C10.S1.XMD6.m1ldec
		Property / Symbols used
			Q11443
		Property / Symbols used: Q11443 / rank
			Normal rank
		Property / Symbols used: Q11443 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\chi(\ell)}}$ \chi(\ell)
		Property / Symbols used: Q11443 / qualifier
			xml-id: C10.S17.XMD5.m1dec

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Latest revision as of 15:32, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:10.17.E15	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle\mathcal{V}_{z,i\infty}\left(t^{-\ell}\right)\leq\begin{cases}|z|^{-\ell},&0\leq\operatorname{ph}z\leq\pi,\\ \chi(\ell)|z|^{-\ell},&\parbox[t]{224.037pt}{$-\tfrac{1}{2}\pi\leq\operatorname{ph}z\leq 0$ or $\pi\leq\operatorname{ph}z\leq\tfrac{3}{2}\pi$,}\\ 2\chi(\ell)|\Im z|^{-\ell},&\parbox[t]{224.037pt}{$-\pi<\operatorname{ph}z\leq-\tfrac{1}{2}\pi$ or $\tfrac{3}{2}\pi\leq\operatorname{ph}z<2\pi$,}\end{cases}}}$

0 references

DLMF id

DLMF:10.17.E15

0 references

Symbols used

the ratio of the circumference of a circle to its diameter

Defining formula

${\displaystyle{\displaystyle\pi}}$

xml-id

C3.S12.E1.m2ajdec

0 references

Q10901

Defining formula

${\displaystyle{\displaystyle\Im}}$

xml-id

C1.S9.E2.m2adec

0 references

imaginary unit

Defining formula

${\displaystyle{\displaystyle\mathrm{i}}}$

xml-id

C1.S9.E1.m2agdec

0 references

Q10817

Defining formula

${\displaystyle{\displaystyle\operatorname{ph}}}$

xml-id

C1.S9.E7.m1aidec

0 references

total variation

Defining formula

${\displaystyle{\displaystyle\mathcal{V}_{\NVar{a,b}}\left(\NVar{f}\right)}}$

xml-id

C1.S4.E33.m2aadec

0 references

Q11426

Defining formula

${\displaystyle{\displaystyle z}}$

xml-id

C10.S1.XMD6.m1ldec

0 references

Q11443

Defining formula

${\displaystyle{\displaystyle\chi(\ell)}}$

xml-id

C10.S17.XMD5.m1dec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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