DLMF:14.23.E2 (Q4948): Difference between revisions

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Revision as of 13:38, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 13:38, 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
			base of natural logarithm
		Property / Symbols used: base of natural logarithm / rank
			Normal rank
		Property / Symbols used: base of natural logarithm / qualifier
			Defining formula: ${\displaystyle{\displaystyle\mathrm{e}}}$ \expe
		Property / Symbols used: base of natural logarithm / qualifier
			xml-id: C4.S2.E11.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.m2aadec
		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

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Latest revision as of 13:38, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:14.23.E2	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle\boldsymbol{Q}^{\mu}_{\nu}\left(x\pm i0\right)=\frac{e^{\pm\mu\pi i/2}}{\Gamma\left(\nu+\mu+1\right)}\left(\mathsf{Q}^{\mu}_{\nu}\left(x\right)\mp\tfrac{1}{2}\pi i\mathsf{P}^{\mu}_{\nu}\left(x\right)\right).}}$

0 references

DLMF id

DLMF:14.23.E2

0 references

Symbols used

gamma function

Defining formula

${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$

xml-id

C5.S2.E1.m2adec

0 references

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

Q11592

Defining formula

${\displaystyle{\displaystyle\boldsymbol{Q}^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{z}\right)}}$

xml-id

C14.S21.SS1.p1.m3adec

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

base of natural logarithm

Defining formula

${\displaystyle{\displaystyle\mathrm{e}}}$

xml-id

C4.S2.E11.m2aadec

0 references

imaginary unit

Defining formula

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

xml-id

C1.S9.E1.m2aadec

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

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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