DLMF:10.38.E2 (Q3561): Difference between revisions

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Revision as of 13:49, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 13:49, 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
			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.m2adec
		Property / Symbols used
			Q11245
		Property / Symbols used: Q11245 / rank
			Normal rank
		Property / Symbols used: Q11245 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\notin}}$ \notin
		Property / Symbols used: Q11245 / qualifier
			xml-id: introduction.Sx4.p1.t1.r11.m2adec
		Property / Symbols used
			partial derivative of $$f$$ with respect to $$x$$
		Property / Symbols used: partial derivative of $$f$$ with respect to $$x$$ / rank
			Normal rank
		Property / Symbols used: partial derivative of $$f$$ with respect to $$x$$ / qualifier
			Defining formula: ${\displaystyle{\displaystyle\frac{\partial\NVar{f}}{\partial\NVar{x}}}}$ \pderiv{\NVar{f}}{\NVar{x}}
		Property / Symbols used: partial derivative of $$f$$ with respect to $$x$$ / qualifier
			xml-id: C1.S5.E3.m4aadec
		Property / Symbols used
			partial differential of $$x$$
		Property / Symbols used: partial differential of $$x$$ / rank
			Normal rank
		Property / Symbols used: partial differential of $$x$$ / qualifier
			Defining formula: ${\displaystyle{\displaystyle\partial\NVar{x}}}$ \pdiff{\NVar{x}}
		Property / Symbols used: partial differential of $$x$$ / qualifier
			xml-id: C1.S5.E3.m2aadec
		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.m1adec
		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.m1adec

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Latest revision as of 13:49, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:10.38.E2	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle\frac{\partial K_{\nu}\left(z\right)}{\partial\nu}=\tfrac{1}{2}\pi\csc\left(\nu\pi\right)\*\left(\frac{\partial I_{-\nu}\left(z\right)}{\partial\nu}-\frac{\partial I_{\nu}\left(z\right)}{\partial\nu}\right)-\pi\cot\left(\nu\pi\right)K_{\nu}\left(z\right),}}$

0 references

DLMF id

DLMF:10.38.E2

0 references

constraint

${\displaystyle{\displaystyle\nu\notin\mathbb{Z}}}$

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.m2adec

0 references

cosecant function

Defining formula

${\displaystyle{\displaystyle\csc\NVar{z}}}$

xml-id

C4.S14.E5.m2adec

0 references

cotangent function

Defining formula

${\displaystyle{\displaystyle\cot\NVar{z}}}$

xml-id

C4.S14.E7.m2adec

0 references

Q10818

Defining formula

${\displaystyle{\displaystyle\mathbb{Z}}}$

xml-id

introduction.Sx4.p2.t1.r20.m2adec

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.m2aadec

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.m2adec

0 references

Q11245

Defining formula

${\displaystyle{\displaystyle\notin}}$

xml-id

introduction.Sx4.p1.t1.r11.m2adec

0 references

partial derivative of $$f$$ with respect to $$x$$

Defining formula

${\displaystyle{\displaystyle\frac{\partial\NVar{f}}{\partial\NVar{x}}}}$

xml-id

C1.S5.E3.m4aadec

0 references

partial differential of $$x$$

Defining formula

${\displaystyle{\displaystyle\partial\NVar{x}}}$

xml-id

C1.S5.E3.m2aadec

0 references

Q11426

Defining formula

${\displaystyle{\displaystyle z}}$

xml-id

C10.S1.XMD6.m1adec

0 references

Q11427

Defining formula

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

xml-id

C10.S1.XMD7.m1adec

0 references

 

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