DLMF:10.43.E25 (Q3639): Difference between revisions

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Revision as of 14:03, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 14:03, 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
			exponential function
		Property / Symbols used: exponential function / rank
			Normal rank
		Property / Symbols used: exponential function / qualifier
			Defining formula: ${\displaystyle{\displaystyle\exp\NVar{z}}}$ \exp@@{\NVar{z}}
		Property / Symbols used: exponential function / qualifier
			xml-id: C4.S2.E19.m2abdec
		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.m3atdec
		Property / Symbols used
			modified Bessel function of the second kind
		Property / Symbols used: modified Bessel function of the second kind / rank
			Normal rank
		Property / Symbols used: modified Bessel function of the second kind / qualifier
			Defining formula: ${\displaystyle{\displaystyle K_{\NVar{\nu}}\left(\NVar{z}\right)}}$ \modBesselK{\NVar{\nu}}@{\NVar{z}}
		Property / Symbols used: modified Bessel function of the second kind / qualifier
			xml-id: C10.S25.E3.m2akdec
		Property / Symbols used
			Q10811
		Property / Symbols used: Q10811 / rank
			Normal rank
		Property / Symbols used: Q10811 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\Re}}$ \realpart@@
		Property / Symbols used: Q10811 / qualifier
			xml-id: C1.S9.E2.m1ahdec
		Property / Symbols used
			secant function
		Property / Symbols used: secant function / rank
			Normal rank
		Property / Symbols used: secant function / qualifier
			Defining formula: ${\displaystyle{\displaystyle\sec\NVar{z}}}$ \sec@@{\NVar{z}}
		Property / Symbols used: secant function / qualifier
			xml-id: C4.S14.E6.m2aadec
		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.m1ldec

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Latest revision as of 14:03, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:10.43.E25	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle\int_{0}^{\infty}K_{\nu}\left(bt\right)\exp\left(-p^{2}t^{2}\right)\mathrm{d}t=\frac{\sqrt{\pi}}{4p}\sec\left(\tfrac{1}{2}\pi\nu\right)\exp\left(\frac{b^{2}}{8p^{2}}\right)K_{\frac{1}{2}\nu}\left(\frac{b^{2}}{8p^{2}}\right),}}$

0 references

DLMF id

DLMF:10.43.E25

0 references

constraint

${\displaystyle{\displaystyle|\Re\nu|<1}}$

0 references

${\displaystyle{\displaystyle\Re(p^{2})>0}}$

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.m2agdec

0 references

Q10770

Defining formula

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

xml-id

C1.S4.SS4.m1atdec

0 references

exponential function

Defining formula

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

xml-id

C4.S2.E19.m2abdec

0 references

Q10771

Defining formula

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

xml-id

C1.S4.SS4.m3atdec

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

Q10811

Defining formula

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

xml-id

C1.S9.E2.m1ahdec

0 references

secant function

Defining formula

${\displaystyle{\displaystyle\sec\NVar{z}}}$

xml-id

C4.S14.E6.m2aadec

0 references

Q11427

Defining formula

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

xml-id

C10.S1.XMD7.m1ldec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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