DLMF:10.32.E18 (Q3538): Difference between revisions

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Revision as of 13:45, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 13:45, 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
			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.m1aidec
		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.m1ndec
		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.m1mdec

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Latest revision as of 13:45, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:10.32.E18	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle K_{\nu}\left(z\right)K_{\nu}\left(\zeta\right)=\frac{1}{2}\int_{0}^{\infty}\exp\left(-\frac{t}{2}-\frac{z^{2}+\zeta^{2}}{2t}\right)K_{\nu}\left(\frac{z\zeta}{t}\right)\frac{\mathrm{d}t}{t},}}$

0 references

DLMF id

DLMF:10.32.E18

0 references

constraint

${\displaystyle{\displaystyle|\operatorname{ph}z|<\pi}}$

0 references

${\displaystyle{\displaystyle|\operatorname{ph}\zeta|<\pi}}$

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${\displaystyle{\displaystyle|\operatorname{ph}\left(z+\zeta\right)|<\tfrac{1}{4}\pi}}$

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.m2aodec

0 references

Q10770

Defining formula

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

xml-id

C1.S4.SS4.m1aqdec

0 references

exponential function

Defining formula

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

xml-id

C4.S2.E19.m2aadec

0 references

Q10771

Defining formula

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

xml-id

C1.S4.SS4.m3aqdec

0 references

modified Bessel function of the second kind

Defining formula

${\displaystyle{\displaystyle K_{\NVar{\nu}}\left(\NVar{z}\right)}}$

xml-id

C10.S25.E3.m2akdec

0 references

Q10817

Defining formula

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

xml-id

C1.S9.E7.m1aidec

0 references

Q11426

Defining formula

${\displaystyle{\displaystyle z}}$

xml-id

C10.S1.XMD6.m1ndec

0 references

Q11427

Defining formula

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

xml-id

C10.S1.XMD7.m1mdec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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