DLMF:11.6.E3 (Q3979): Difference between revisions

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Revision as of 14:46, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 14:46, 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
			the ratio of the circumference of a circle to its diameter
		Property / Symbols used: the ratio of the circumference of a circle to its diameter / rank
			Normal rank
		Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
			Defining formula: ${\displaystyle{\displaystyle\pi}}$ \cpi
		Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
			xml-id: C3.S12.E1.m2abdec
		Property / Symbols used
			Q10770
		Property / Symbols used: Q10770 / rank
			Normal rank
		Property / Symbols used: Q10770 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$ \diff{\NVar{x}}
		Property / Symbols used: Q10770 / qualifier
			xml-id: C1.S4.SS4.m1adec
		Property / Symbols used
			Q10755
		Property / Symbols used: Q10755 / rank
			Normal rank
		Property / Symbols used: Q10755 / qualifier
			Defining formula: ${\displaystyle{\displaystyle!}}$ !
		Property / Symbols used: Q10755 / qualifier
			xml-id: introduction.Sx4.p1.t1.r15.m5adec
		Property / Symbols used
			Q10771
		Property / Symbols used: Q10771 / rank
			Normal rank
		Property / Symbols used: Q10771 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\int}}$ \int
		Property / Symbols used: Q10771 / qualifier
			xml-id: C1.S4.SS4.m3adec
		Property / Symbols used
			principal branch of logarithm function
		Property / Symbols used: principal branch of logarithm function / rank
			Normal rank
		Property / Symbols used: principal branch of logarithm function / qualifier
			Defining formula: ${\displaystyle{\displaystyle\ln\NVar{z}}}$ \ln@@{\NVar{z}}
		Property / Symbols used: principal branch of logarithm function / qualifier
			xml-id: C4.S2.E2.m2adec
		Property / Symbols used
			Q10817
		Property / Symbols used: Q10817 / rank
			Normal rank
		Property / Symbols used: Q10817 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\operatorname{ph}}}$ \phase
		Property / Symbols used: Q10817 / qualifier
			xml-id: C1.S9.E7.m1abdec
		Property / Symbols used
			Q11491
		Property / Symbols used: Q11491 / rank
			Normal rank
		Property / Symbols used: Q11491 / qualifier
			Defining formula: ${\displaystyle{\displaystyle z}}$ z
		Property / Symbols used: Q11491 / qualifier
			xml-id: C11.S1.XMD2.m1bdec
		Property / Symbols used
			Q11497
		Property / Symbols used: Q11497 / rank
			Normal rank
		Property / Symbols used: Q11497 / qualifier
			Defining formula: ${\displaystyle{\displaystyle k}}$ k
		Property / Symbols used: Q11497 / qualifier
			xml-id: C11.S1.XMD5.m1bdec
		Property / Symbols used
			Q11498
		Property / Symbols used: Q11498 / rank
			Normal rank
		Property / Symbols used: Q11498 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\delta}}$ \delta
		Property / Symbols used: Q11498 / qualifier
			xml-id: C11.S1.XMD6.m1bdec

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Latest revision as of 14:46, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:11.6.E3	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle\int_{0}^{z}\mathbf{K}_{0}\left(t\right)\mathrm{d}t-\frac{2}{\pi}(\ln\left(2z\right)+\gamma)\sim\frac{2}{\pi}\sum_{k=1}^{\infty}(-1)^{k+1}\frac{(2k)!(2k-1)!}{(k!)^{2}(2z)^{2k}},}}$

0 references

DLMF id

DLMF:11.6.E3

0 references

constraint

${\displaystyle{\displaystyle|\operatorname{ph}z|\leq\pi-\delta}}$

0 references

Symbols used

Euler’s constant

Defining formula

${\displaystyle{\displaystyle\gamma}}$

xml-id

C5.S2.E3.m2adec

0 references

Struve function

Defining formula

${\displaystyle{\displaystyle\mathbf{K}_{\NVar{\nu}}\left(\NVar{z}\right)}}$

xml-id

C11.S2.E5.m2aadec

0 references

Q10931

Defining formula

${\displaystyle{\displaystyle\sim}}$

xml-id

C2.S1.SS3.p1.m11abdec

0 references

the ratio of the circumference of a circle to its diameter

Defining formula

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

xml-id

C3.S12.E1.m2abdec

0 references

Q10770

Defining formula

${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$

xml-id

C1.S4.SS4.m1adec

0 references

Q10755

Defining formula

${\displaystyle{\displaystyle!}}$

xml-id

introduction.Sx4.p1.t1.r15.m5adec

0 references

Q10771

Defining formula

${\displaystyle{\displaystyle\int}}$

xml-id

C1.S4.SS4.m3adec

0 references

principal branch of logarithm function

Defining formula

${\displaystyle{\displaystyle\ln\NVar{z}}}$

xml-id

C4.S2.E2.m2adec

0 references

Q10817

Defining formula

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

xml-id

C1.S9.E7.m1abdec

0 references

Q11491

Defining formula

${\displaystyle{\displaystyle z}}$

xml-id

C11.S1.XMD2.m1bdec

0 references

Q11497

Defining formula

${\displaystyle{\displaystyle k}}$

xml-id

C11.S1.XMD5.m1bdec

0 references

Q11498

Defining formula

${\displaystyle{\displaystyle\delta}}$

xml-id

C11.S1.XMD6.m1bdec

0 references

 

Sitelinks

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DRMF related sites(0 entries)

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