DLMF:14.20.E11 (Q4932): Difference between revisions

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Revision as of 13:34, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 13:34, 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.m2agdec
		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.m1aadec
		Property / Symbols used
			hyperbolic sine function
		Property / Symbols used: hyperbolic sine function / rank
			Normal rank
		Property / Symbols used: hyperbolic sine function / qualifier
			Defining formula: ${\displaystyle{\displaystyle\sinh\NVar{z}}}$ \sinh@@{\NVar{z}}
		Property / Symbols used: hyperbolic sine function / qualifier
			xml-id: C4.S28.E1.m2addec
		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.m2aqdec
		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.m3aadec
		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.m1pdec
		Property / Symbols used
			Q11630
		Property / Symbols used: Q11630 / rank
			Normal rank
		Property / Symbols used: Q11630 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\tau}}$ \tau
		Property / Symbols used: Q11630 / qualifier
			xml-id: C14.S1.XMD3.m1rdec
		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.m1hdec

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Latest revision as of 13:34, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:14.20.E11	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle f(\tau)=\frac{\tau}{\pi}\sinh\left(\tau\pi\right)\Gamma\left(\tfrac{1}{2}-\mu+i\tau\right)\*\Gamma\left(\tfrac{1}{2}-\mu-i\tau\right)\int_{1}^{\infty}P^{\mu}_{-\frac{1}{2}+i\tau}\left(x\right)g(x)\mathrm{d}x,}}$

0 references

DLMF id

DLMF:14.20.E11

0 references

Symbols used

gamma function

Defining formula

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

xml-id

C5.S2.E1.m2aedec

0 references

Q11481

Defining formula

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

xml-id

C14.S21.SS1.p1.m1aadec

0 references

the ratio of the circumference of a circle to its diameter

Defining formula

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

xml-id

C3.S12.E1.m2agdec

0 references

Q10770

Defining formula

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

xml-id

C1.S4.SS4.m1aadec

0 references

hyperbolic sine function

Defining formula

${\displaystyle{\displaystyle\sinh\NVar{z}}}$

xml-id

C4.S28.E1.m2addec

0 references

imaginary unit

Defining formula

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

xml-id

C1.S9.E1.m2aqdec

0 references

Q10771

Defining formula

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

xml-id

C1.S4.SS4.m3aadec

0 references

Q11589

Defining formula

${\displaystyle{\displaystyle x}}$

xml-id

C14.S1.XMD1.m1pdec

0 references

Q11630

Defining formula

${\displaystyle{\displaystyle\tau}}$

xml-id

C14.S1.XMD3.m1rdec

0 references

Q11591

Defining formula

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

xml-id

C14.S1.XMD7.m1hdec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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