DLMF:16.17.E1 (Q5277): Difference between revisions

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Revision as of 15:54, 29 December 2019 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Created a new Item: Wikidata Toolkit example test item creation		Latest revision as of 14:42, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint
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		Property / Symbols defined
			Meijer $$G$$ -function
		Property / Symbols defined: Meijer $$G$$ -function / rank
			Normal rank
		Property / Symbols used
			gamma function
		Property / Symbols used: gamma function / rank
			Normal rank
		Property / Symbols used: gamma function / qualifier
			Defining formula: ${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$ \EulerGamma@{\NVar{z}}
		Property / Symbols used: gamma function / qualifier
			xml-id: C5.S2.E1.m2adec
		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
			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.m1adec
		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.m2adec
		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.m3adec
		Property / Symbols used
			Q11690
		Property / Symbols used: Q11690 / rank
			Normal rank
		Property / Symbols used: Q11690 / qualifier
			Defining formula: ${\displaystyle{\displaystyle p}}$ p
		Property / Symbols used: Q11690 / qualifier
			xml-id: C16.S1.XMD1.m1dec
		Property / Symbols used
			Q11691
		Property / Symbols used: Q11691 / rank
			Normal rank
		Property / Symbols used: Q11691 / qualifier
			Defining formula: ${\displaystyle{\displaystyle q}}$ q
		Property / Symbols used: Q11691 / qualifier
			xml-id: C16.S1.XMD2.m1dec
		Property / Symbols used
			Q11692
		Property / Symbols used: Q11692 / rank
			Normal rank
		Property / Symbols used: Q11692 / qualifier
			Defining formula: ${\displaystyle{\displaystyle z}}$ z
		Property / Symbols used: Q11692 / qualifier
			xml-id: C16.S1.XMD3.m1dec
		Property / Symbols used
			Q11693
		Property / Symbols used: Q11693 / rank
			Normal rank
		Property / Symbols used: Q11693 / qualifier
			Defining formula: ${\displaystyle{\displaystyle a,a_{1},\ldots,a_{p}}}$ a,a_{1},\ldots,a_{p}
		Property / Symbols used: Q11693 / qualifier
			xml-id: C16.S1.XMD4.m1dec
		Property / Symbols used
			Q11694
		Property / Symbols used: Q11694 / rank
			Normal rank
		Property / Symbols used: Q11694 / qualifier
			Defining formula: ${\displaystyle{\displaystyle b,b_{1},\ldots,b_{q}}}$ b,b_{1},\ldots,b_{q}
		Property / Symbols used: Q11694 / qualifier
			xml-id: C16.S1.XMD5.m1dec

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Latest revision as of 14:42, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:16.17.E1	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle{G^{m,n}_{p,q}}\left(z;\mathbf{a};\mathbf{b}\right)={G^{m,n}_{p,q}}\left(z;{a_{1},\dots,a_{p}\atop b_{1},\dots,b_{q}}\right)=\frac{1}{2\pi\mathrm{i}}\int_{L}\left({\textstyle\ifrac{\prod\limits_{\ell=1}^{m}\Gamma\left(b_{\ell}-s\right)\prod\limits_{\ell=1}^{n}\Gamma\left(1-a_{\ell}+s\right)}{\left(\prod\limits_{\ell=m}^{q-1}\Gamma\left(1-b_{\ell+1}+s\right)\prod\limits_{\ell=n}^{p-1}\Gamma\left(a_{\ell+1}-s\right)\right)}}\right)z^{s}\mathrm{d}s,}}$

0 references

DLMF id

DLMF:16.17.E1

0 references

Symbols defined

Meijer $$G$$ -function

0 references

Symbols used

gamma function

Defining formula

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

xml-id

C5.S2.E1.m2adec

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

Q10770

Defining formula

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

xml-id

C1.S4.SS4.m1adec

0 references

imaginary unit

Defining formula

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

xml-id

C1.S9.E1.m2adec

0 references

Q10771

Defining formula

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

xml-id

C1.S4.SS4.m3adec

0 references

Q11690

Defining formula

${\displaystyle{\displaystyle p}}$

xml-id

C16.S1.XMD1.m1dec

0 references

Q11691

Defining formula

${\displaystyle{\displaystyle q}}$

xml-id

C16.S1.XMD2.m1dec

0 references

Q11692

Defining formula

${\displaystyle{\displaystyle z}}$

xml-id

C16.S1.XMD3.m1dec

0 references

Q11693

Defining formula

${\displaystyle{\displaystyle a,a_{1},\ldots,a_{p}}}$

xml-id

C16.S1.XMD4.m1dec

0 references

Q11694

Defining formula

${\displaystyle{\displaystyle b,b_{1},\ldots,b_{q}}}$

xml-id

C16.S1.XMD5.m1dec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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