DLMF:10.67.E7 (Q3852): Difference between revisions

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Revision as of 14:26, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 14:26, 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
			base of natural logarithm
		Property / Symbols used: base of natural logarithm / rank
			Normal rank
		Property / Symbols used: base of natural logarithm / qualifier
			Defining formula: ${\displaystyle{\displaystyle\mathrm{e}}}$ \expe
		Property / Symbols used: base of natural logarithm / qualifier
			xml-id: C4.S2.E11.m2afdec
		Property / Symbols used
			sine function
		Property / Symbols used: sine function / rank
			Normal rank
		Property / Symbols used: sine function / qualifier
			Defining formula: ${\displaystyle{\displaystyle\sin\NVar{z}}}$ \sin@@{\NVar{z}}
		Property / Symbols used: sine function / qualifier
			xml-id: C4.S14.E1.m2addec
		Property / Symbols used
			Q11428
		Property / Symbols used: Q11428 / rank
			Normal rank
		Property / Symbols used: Q11428 / qualifier
			Defining formula: ${\displaystyle{\displaystyle k}}$ k
		Property / Symbols used: Q11428 / qualifier
			xml-id: C10.S1.XMD3.m1fdec
		Property / Symbols used
			Q11435
		Property / Symbols used: Q11435 / rank
			Normal rank
		Property / Symbols used: Q11435 / qualifier
			Defining formula: ${\displaystyle{\displaystyle x}}$ x
		Property / Symbols used: Q11435 / qualifier
			xml-id: C10.S1.XMD4.m1fdec
		Property / Symbols used
			Q11427
		Property / Symbols used: Q11427 / rank
			Normal rank
		Property / Symbols used: Q11427 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\nu}}$ \nu
		Property / Symbols used: Q11427 / qualifier
			xml-id: C10.S1.XMD7.m1fdec
		Property / Symbols used
			expansion (locally)
		Property / Symbols used: expansion (locally) / rank
			Normal rank
		Property / Symbols used: expansion (locally) / qualifier
			Defining formula: ${\displaystyle{\displaystyle b_{k}(\nu)}}$ b_{k}(\nu)
		Property / Symbols used: expansion (locally) / qualifier
			xml-id: C10.S17.XMD3.m1bdec

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Latest revision as of 14:26, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:10.67.E7	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle\operatorname{ber}_{\nu}'x\sim\frac{e^{x/\sqrt{2}}}{(2\pi x)^{\frac{1}{2}}}\*\sum_{k=0}^{\infty}\frac{b_{k}(\nu)}{x^{k}}\cos\left(\frac{x}{\sqrt{2}}+\left(\frac{\nu}{2}+\frac{3k}{4}+\frac{1}{8}\right)\pi\right)-\frac{1}{\pi}(\sin\left(2\nu\pi\right)\operatorname{ker}_{\nu}'x+\cos\left(2\nu\pi\right)\operatorname{kei}_{\nu}'x),}}$

0 references

DLMF id

DLMF:10.67.E7

0 references

Symbols used

Kelvin function

Defining formula

${\displaystyle{\displaystyle\operatorname{ber}_{\NVar{\nu}}\left(\NVar{x}\right)}}$

xml-id

C10.S61.E1.m2aadec

0 references

Kelvin function

Defining formula

${\displaystyle{\displaystyle\operatorname{kei}_{\NVar{\nu}}\left(\NVar{x}\right)}}$

xml-id

C10.S61.E2.m3addec

0 references

Kelvin function

Defining formula

${\displaystyle{\displaystyle\operatorname{ker}_{\NVar{\nu}}\left(\NVar{x}\right)}}$

xml-id

C10.S61.E2.m2addec

0 references

Q10931

Defining formula

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

xml-id

C2.S1.SS3.p1.m11afdec

0 references

the ratio of the circumference of a circle to its diameter

Defining formula

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

xml-id

C3.S12.E1.m2afdec

0 references

cosine function

Defining formula

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

xml-id

C4.S14.E2.m2addec

0 references

base of natural logarithm

Defining formula

${\displaystyle{\displaystyle\mathrm{e}}}$

xml-id

C4.S2.E11.m2afdec

0 references

sine function

Defining formula

${\displaystyle{\displaystyle\sin\NVar{z}}}$

xml-id

C4.S14.E1.m2addec

0 references

Q11428

Defining formula

${\displaystyle{\displaystyle k}}$

xml-id

C10.S1.XMD3.m1fdec

0 references

Q11435

Defining formula

${\displaystyle{\displaystyle x}}$

xml-id

C10.S1.XMD4.m1fdec

0 references

Q11427

Defining formula

${\displaystyle{\displaystyle\nu}}$

xml-id

C10.S1.XMD7.m1fdec

0 references

expansion (locally)

Defining formula

${\displaystyle{\displaystyle b_{k}(\nu)}}$

xml-id

C10.S17.XMD3.m1bdec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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