DLMF:10.9.E28 (Q3098): Difference between revisions

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Revision as of 15:17, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 15:18, 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.m2aaadec
		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.m1aaadec
		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.m2aadec
		Property / Symbols used
			imaginary unit
		Property / Symbols used: imaginary unit / rank
			Normal rank
		Property / Symbols used: imaginary unit / qualifier
			Defining formula: ${\displaystyle{\displaystyle\mathrm{i}}}$ \iunit
		Property / Symbols used: imaginary unit / qualifier
			xml-id: C1.S9.E1.m2andec
		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.m3aaadec
		Property / Symbols used
			modified Bessel function of the first kind
		Property / Symbols used: modified Bessel function of the first kind / rank
			Normal rank
		Property / Symbols used: modified Bessel function of the first kind / qualifier
			Defining formula: ${\displaystyle{\displaystyle I_{\NVar{\nu}}\left(\NVar{z}\right)}}$ \modBesselI{\NVar{\nu}}@{\NVar{z}}
		Property / Symbols used: modified Bessel function of the first kind / qualifier
			xml-id: C10.S25.E2.m2adec
		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.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.m1wdec
		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.m1wdec
		Property / Symbols used
			Q11437
		Property / Symbols used: Q11437 / rank
			Normal rank
		Property / Symbols used: Q11437 / qualifier
			Defining formula: ${\displaystyle{\displaystyle c}}$ c
		Property / Symbols used: Q11437 / qualifier
			xml-id: C10.S9.XMD2.m1dec

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Latest revision as of 15:18, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:10.9.E28	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle J_{\nu}\left(z\right)J_{\nu}\left(\zeta\right)=\frac{1}{2\pi i}\int_{c-i\infty}^{c+i\infty}\*\exp\left(\frac{1}{2}t-\frac{z^{2}+\zeta^{2}}{2t}\right)I_{\nu}\left(\frac{z\zeta}{t}\right)\frac{\mathrm{d}t}{t},}}$

0 references

DLMF id

DLMF:10.9.E28

0 references

constraint

${\displaystyle{\displaystyle\Re\nu>-1}}$

0 references

Symbols used

Bessel function of the first kind

Defining formula

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

xml-id

C10.S2.E2.m2aodec

0 references

the ratio of the circumference of a circle to its diameter

Defining formula

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

xml-id

C3.S12.E1.m2aaadec

0 references

Q10770

Defining formula

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

xml-id

C1.S4.SS4.m1aaadec

0 references

exponential function

Defining formula

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

xml-id

C4.S2.E19.m2aadec

0 references

imaginary unit

Defining formula

${\displaystyle{\displaystyle\mathrm{i}}}$

xml-id

C1.S9.E1.m2andec

0 references

Q10771

Defining formula

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

xml-id

C1.S4.SS4.m3aaadec

0 references

modified Bessel function of the first kind

Defining formula

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

xml-id

C10.S25.E2.m2adec

0 references

Q10811

Defining formula

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

xml-id

C1.S9.E2.m1aidec

0 references

Q11426

Defining formula

${\displaystyle{\displaystyle z}}$

xml-id

C10.S1.XMD6.m1wdec

0 references

Q11427

Defining formula

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

xml-id

C10.S1.XMD7.m1wdec

0 references

Q11437

Defining formula

${\displaystyle{\displaystyle c}}$

xml-id

C10.S9.XMD2.m1dec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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