DLMF:15.10.E16 (Q5132): Difference between revisions

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Revision as of 15:49, 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 14:15, 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
			$$={{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$ Gauss’ hypergeometric function
		Property / Symbols used: $$={{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$ Gauss’ hypergeometric function / rank
			Normal rank
		Property / Symbols used: $$={{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$ Gauss’ hypergeometric function / qualifier
			Defining formula: ${\displaystyle{\displaystyle F\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)}}$ \hyperF@{\NVar{a}}{\NVar{b}}{\NVar{c}}{\NVar{z}}
		Property / Symbols used: $$={{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$ Gauss’ hypergeometric function / qualifier
			xml-id: C15.S2.E1.m2akdec
		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
			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
			Q11644
		Property / Symbols used: Q11644 / rank
			Normal rank
		Property / Symbols used: Q11644 / qualifier
			Defining formula: ${\displaystyle{\displaystyle z}}$ z
		Property / Symbols used: Q11644 / qualifier
			xml-id: C15.S1.XMD3.m1odec
		Property / Symbols used
			Q11645
		Property / Symbols used: Q11645 / rank
			Normal rank
		Property / Symbols used: Q11645 / qualifier
			Defining formula: ${\displaystyle{\displaystyle a}}$ a
		Property / Symbols used: Q11645 / qualifier
			xml-id: C15.S1.XMD4.m1odec
		Property / Symbols used
			Q11646
		Property / Symbols used: Q11646 / rank
			Normal rank
		Property / Symbols used: Q11646 / qualifier
			Defining formula: ${\displaystyle{\displaystyle b}}$ b
		Property / Symbols used: Q11646 / qualifier
			xml-id: C15.S1.XMD5.m1odec
		Property / Symbols used
			Q11647
		Property / Symbols used: Q11647 / rank
			Normal rank
		Property / Symbols used: Q11647 / qualifier
			Defining formula: ${\displaystyle{\displaystyle c}}$ c
		Property / Symbols used: Q11647 / qualifier
			xml-id: C15.S1.XMD6.m1ldec
		Property / Symbols used
			Q11667
		Property / Symbols used: Q11667 / rank
			Normal rank
		Property / Symbols used: Q11667 / qualifier
			Defining formula: ${\displaystyle{\displaystyle w_{m}(z)}}$ w_{m}(z)
		Property / Symbols used: Q11667 / qualifier
			xml-id: C15.S10.XMD2.m1edec

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Latest revision as of 14:15, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:15.10.E16	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle w_{6}(z)=e^{b\pi\mathrm{i}}z^{-b}F\left({b,b-c+1\atop b-a+1};\frac{1}{z}\right)=e^{(c-a)\pi\mathrm{i}}z^{a-c}(1-z)^{c-a-b}\*F\left({1-a,c-a\atop b-a+1};\frac{1}{z}\right)=(1-z)^{-b}F\left({b,c-a\atop b-a+1};\frac{1}{1-z}\right)=e^{(c-1)\pi\mathrm{i}}z^{1-c}(1-z)^{c-b-1}\*F\left({1-a,b-c+1\atop b-a+1};\frac{1}{1-z}\right).}}$

0 references

DLMF id

DLMF:15.10.E16

0 references

Symbols used

$$={{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$ Gauss’ hypergeometric function

Defining formula

${\displaystyle{\displaystyle F\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)}}$

xml-id

C15.S2.E1.m2akdec

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

Q11644

Defining formula

${\displaystyle{\displaystyle z}}$

xml-id

C15.S1.XMD3.m1odec

0 references

Q11645

Defining formula

${\displaystyle{\displaystyle a}}$

xml-id

C15.S1.XMD4.m1odec

0 references

Q11646

Defining formula

${\displaystyle{\displaystyle b}}$

xml-id

C15.S1.XMD5.m1odec

0 references

Q11647

Defining formula

${\displaystyle{\displaystyle c}}$

xml-id

C15.S1.XMD6.m1ldec

0 references

Q11667

Defining formula

${\displaystyle{\displaystyle w_{m}(z)}}$

xml-id

C15.S10.XMD2.m1edec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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