DLMF:9.7.E17 (Q2826): Difference between revisions

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Revision as of 14:35, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 14:35, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint
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		Property / Symbols used
			change of variable (locally)
		Property / Symbols used: change of variable (locally) / rank
			Normal rank
		Property / Symbols used: change of variable (locally) / qualifier
			Defining formula: ${\displaystyle{\displaystyle\zeta}}$ \zeta
		Property / Symbols used: change of variable (locally) / qualifier
			xml-id: C9.S7.XMD1.m1kdec
		Property / Symbols used
			function (locally)
		Property / Symbols used: function (locally) / rank
			Normal rank
		Property / Symbols used: function (locally) / qualifier
			Defining formula: ${\displaystyle{\displaystyle\chi(x)}}$ \chi(x)
		Property / Symbols used: function (locally) / qualifier
			xml-id: C9.S7.XMD4.m1ddec
		Property / Symbols used
			Q11389
		Property / Symbols used: Q11389 / rank
			Normal rank
		Property / Symbols used: Q11389 / qualifier
			Defining formula: ${\displaystyle{\displaystyle n}}$ n
		Property / Symbols used: Q11389 / qualifier
			xml-id: C9.S7.XMD8.m1dec
		Property / Symbols used
			Q11390
		Property / Symbols used: Q11390 / rank
			Normal rank
		Property / Symbols used: Q11390 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\sigma}}$ \sigma
		Property / Symbols used: Q11390 / qualifier
			xml-id: C9.S7.XMD9.m1dec

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Latest revision as of 14:35, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:9.7.E17	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle\begin{cases}1,&|\operatorname{ph}z|\leq\tfrac{1}{3}\pi,\\ \min\left(|\csc\left(\operatorname{ph}\zeta\right)|,\chi(n+\sigma)+1\right),&\tfrac{1}{3}\pi\leq|\operatorname{ph}z|\leq\tfrac{2}{3}\pi,\\ \frac{\sqrt{2\pi(n+\sigma)}}{|\cos\left(\operatorname{ph}\zeta\right)|^{n+\sigma}}+\chi(n+\sigma)+1,&\tfrac{2}{3}\pi\leq|\operatorname{ph}z|<\pi,\end{cases}}}$

0 references

DLMF id

DLMF:9.7.E17

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.m2andec

0 references

cosecant function

Defining formula

${\displaystyle{\displaystyle\csc\NVar{z}}}$

xml-id

C4.S14.E5.m2adec

0 references

cosine function

Defining formula

${\displaystyle{\displaystyle\cos\NVar{z}}}$

xml-id

C4.S14.E2.m2afdec

0 references

exponential function

Defining formula

${\displaystyle{\displaystyle\exp\NVar{z}}}$

xml-id

C4.S2.E19.m2aadec

0 references

Q10817

Defining formula

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

xml-id

C1.S9.E7.m1ajdec

0 references

Q10811

Defining formula

${\displaystyle{\displaystyle\Re}}$

xml-id

C1.S9.E2.m1adec

0 references

Q11381

Defining formula

${\displaystyle{\displaystyle z}}$

xml-id

C9.S1.XMD3.m1kdec

0 references

change of variable (locally)

Defining formula

${\displaystyle{\displaystyle\zeta}}$

xml-id

C9.S7.XMD1.m1kdec

0 references

function (locally)

Defining formula

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

xml-id

C9.S7.XMD4.m1ddec

0 references

Q11389

Defining formula

${\displaystyle{\displaystyle n}}$

xml-id

C9.S7.XMD8.m1dec

0 references

Q11390

Defining formula

${\displaystyle{\displaystyle\sigma}}$

xml-id

C9.S7.XMD9.m1dec

0 references

 

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