DLMF:10.14.E6 (Q3143): Difference between revisions

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Revision as of 17:17, 30 December 2019 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 15:23, 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
			Bessel function of the first kind
		Property / Symbols used: Bessel function of the first kind / rank
			Normal rank
		Property / Symbols used: Bessel function of the first kind / qualifier
			Defining formula: ${\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}$ \BesselJ{\NVar{\nu}}@{\NVar{z}}
		Property / Symbols used: Bessel function of the first kind / qualifier
			xml-id: C10.S2.E2.m2aedec
		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.m2adec
		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
			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.m1bdec
		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.m1ddec

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Latest revision as of 15:23, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:10.14.E6	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle|J_{\nu}'\left(\nu x\right)|\leq\frac{(1+x^{2})^{\frac{1}{4}}}{x(2\pi\nu)^{\frac{1}{2}}}\frac{x^{\nu}\exp\left(\nu(1-x^{2})^{\frac{1}{2}}\right)}{\left(1+(1-x^{2})^{\frac{1}{2}}\right)^{\nu}},}}$

0 references

DLMF id

DLMF:10.14.E6

0 references

constraint

${\displaystyle{\displaystyle\nu>0,0<x\leq 1}}$

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.m2aedec

0 references

the ratio of the circumference of a circle to its diameter

Defining formula

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

xml-id

C3.S12.E1.m2adec

0 references

exponential function

Defining formula

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

xml-id

C4.S2.E19.m2aadec

0 references

Q11435

Defining formula

${\displaystyle{\displaystyle x}}$

xml-id

C10.S1.XMD4.m1bdec

0 references

Q11427

Defining formula

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

xml-id

C10.S1.XMD7.m1ddec

0 references

 

Sitelinks

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