DLMF:14.11.E2 (Q4818): Difference between revisions

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Revision as of 01:40, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 01:40, 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.m2aadec
		Property / Symbols used
			cosecant function
		Property / Symbols used: cosecant function / rank
			Normal rank
		Property / Symbols used: cosecant function / qualifier
			Defining formula: ${\displaystyle{\displaystyle\csc\NVar{z}}}$ \csc@@{\NVar{z}}
		Property / Symbols used: cosecant function / qualifier
			xml-id: C4.S14.E5.m2adec
		Property / Symbols used
			cotangent function
		Property / Symbols used: cotangent function / rank
			Normal rank
		Property / Symbols used: cotangent function / qualifier
			Defining formula: ${\displaystyle{\displaystyle\cot\NVar{z}}}$ \cot@@{\NVar{z}}
		Property / Symbols used: cotangent function / qualifier
			xml-id: C4.S14.E7.m2aadec
		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
			sine function
		Property / Symbols used: sine function / rank
			Normal rank
		Property / Symbols used: sine function / qualifier
			Defining formula: ${\displaystyle{\displaystyle\sin\NVar{z}}}$ \sin@@{\NVar{z}}
		Property / Symbols used: sine function / qualifier
			xml-id: C4.S14.E1.m2adec
		Property / Symbols used
			Q11589
		Property / Symbols used: Q11589 / rank
			Normal rank
		Property / Symbols used: Q11589 / qualifier
			Defining formula: ${\displaystyle{\displaystyle x}}$ x
		Property / Symbols used: Q11589 / qualifier
			xml-id: C14.S1.XMD1.m1adec
		Property / Symbols used
			Q11591
		Property / Symbols used: Q11591 / rank
			Normal rank
		Property / Symbols used: Q11591 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\mu}}$ \mu
		Property / Symbols used: Q11591 / qualifier
			xml-id: C14.S1.XMD7.m1adec
		Property / Symbols used
			Q11590
		Property / Symbols used: Q11590 / rank
			Normal rank
		Property / Symbols used: Q11590 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\nu}}$ \nu
		Property / Symbols used: Q11590 / qualifier
			xml-id: C14.S1.XMD8.m1adec
		Property / Symbols used
			Q11605
		Property / Symbols used: Q11605 / rank
			Normal rank
		Property / Symbols used: Q11605 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\mathsf{A}_{\nu}^{\mu}(x)}}$ \mathsf{A}_{\nu}^{\mu}(x)
		Property / Symbols used: Q11605 / qualifier
			xml-id: C14.S11.XMD1.m1adec

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Latest revision as of 01:40, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:14.11.E2	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle\frac{\partial}{\partial\nu}\mathsf{Q}^{\mu}_{\nu}\left(x\right)=-\tfrac{1}{2}\pi^{2}\mathsf{P}^{\mu}_{\nu}\left(x\right)+\frac{\pi\sin\left(\mu\pi\right)}{\sin\left(\nu\pi\right)\sin\left((\nu+\mu)\pi\right)}\mathsf{Q}^{\mu}_{\nu}\left(x\right)-\tfrac{1}{2}\cot\left((\nu+\mu)\pi\right)\mathsf{A}_{\nu}^{\mu}(x)+\tfrac{1}{2}\csc\left((\nu+\mu)\pi\right)\mathsf{A}_{\nu}^{\mu}(-x),}}$

0 references

DLMF id

DLMF:14.11.E2

0 references

Symbols used

Ferrers function of the first kind

Defining formula

${\displaystyle{\displaystyle\mathsf{P}^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{x}\right)}}$

xml-id

C14.S3.E1.m2aadec

0 references

Ferrers function of the second kind

Defining formula

${\displaystyle{\displaystyle\mathsf{Q}^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{x}\right)}}$

xml-id

C14.S3.E2.m2adec

0 references

the ratio of the circumference of a circle to its diameter

Defining formula

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

xml-id

C3.S12.E1.m2aadec

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.m2aadec

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

sine function

Defining formula

${\displaystyle{\displaystyle\sin\NVar{z}}}$

xml-id

C4.S14.E1.m2adec

0 references

Q11589

Defining formula

${\displaystyle{\displaystyle x}}$

xml-id

C14.S1.XMD1.m1adec

0 references

Q11591

Defining formula

${\displaystyle{\displaystyle\mu}}$

xml-id

C14.S1.XMD7.m1adec

0 references

Q11590

Defining formula

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

xml-id

C14.S1.XMD8.m1adec

0 references

Q11605

Defining formula

${\displaystyle{\displaystyle\mathsf{A}_{\nu}^{\mu}(x)}}$

xml-id

C14.S11.XMD1.m1adec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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