DLMF:2.6.E52 (Q878): Difference between revisions

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Revision as of 17:18, 1 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 17:18, 1 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint
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		Property / Symbols used
			Q10755
		Property / Symbols used: Q10755 / rank
			Normal rank
		Property / Symbols used: Q10755 / qualifier
			Defining formula: ${\displaystyle{\displaystyle!}}$ !
		Property / Symbols used: Q10755 / qualifier
			xml-id: introduction.Sx4.p1.t1.r15.m5ajdec
		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.m2acdec
		Property / Symbols used
			Q11028
		Property / Symbols used: Q11028 / rank
			Normal rank
		Property / Symbols used: Q11028 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\mu}}$ \mu
		Property / Symbols used: Q11028 / qualifier
			xml-id: C2.S6.XMD14.m1ldec
		Property / Symbols used
			fractional integral (locally)
		Property / Symbols used: fractional integral (locally) / rank
			Normal rank
		Property / Symbols used: fractional integral (locally) / qualifier
			Defining formula: ${\displaystyle{\displaystyle I^{\mu}}}$ I^{\mu}
		Property / Symbols used: fractional integral (locally) / qualifier
			xml-id: C2.S6.XMD15.m1fdec
		Property / Symbols used
			Q11019
		Property / Symbols used: Q11019 / rank
			Normal rank
		Property / Symbols used: Q11019 / qualifier
			Defining formula: ${\displaystyle{\displaystyle f(t)}}$ f(t)
		Property / Symbols used: Q11019 / qualifier
			xml-id: C2.S6.XMD2.m1aadec
		Property / Symbols used
			Q11031
		Property / Symbols used: Q11031 / rank
			Normal rank
		Property / Symbols used: Q11031 / qualifier
			Defining formula: ${\displaystyle{\displaystyle n}}$ n
		Property / Symbols used: Q11031 / qualifier
			xml-id: C2.S6.XMD20.m1jdec
		Property / Symbols used
			Q11036
		Property / Symbols used: Q11036 / rank
			Normal rank
		Property / Symbols used: Q11036 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\delta_{n}(x)}}$ \delta_{n}(x)
		Property / Symbols used: Q11036 / qualifier
			xml-id: C2.S6.XMD25.m1cdec

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Latest revision as of 17:18, 1 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:2.6.E52	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle I^{\mu}f(x)=\sum_{s=0}^{n-1}(-1)^{s}\frac{\Gamma\left(1-s-\alpha\right)}{\Gamma\left(\mu+1-s-\alpha\right)}x^{\mu-s-\alpha}-\frac{\pi}{\sin\left(\pi\alpha\right)}\sum_{s=1}^{n}\frac{1}{\Gamma\left(\mu+1-s\right)}\frac{x^{\mu-s}}{(s-1)!}+\frac{1}{x^{n}}\delta_{n}(x).}}$

0 references

DLMF id

DLMF:2.6.E52

0 references

Symbols used

gamma function

Defining formula

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

xml-id

C5.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.m2afdec

0 references

Q10755

Defining formula

${\displaystyle{\displaystyle!}}$

xml-id

introduction.Sx4.p1.t1.r15.m5ajdec

0 references

sine function

Defining formula

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

xml-id

C4.S14.E1.m2acdec

0 references

Q11028

Defining formula

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

xml-id

C2.S6.XMD14.m1ldec

0 references

fractional integral (locally)

Defining formula

${\displaystyle{\displaystyle I^{\mu}}}$

xml-id

C2.S6.XMD15.m1fdec

0 references

Q11019

Defining formula

${\displaystyle{\displaystyle f(t)}}$

xml-id

C2.S6.XMD2.m1aadec

0 references

Q11031

Defining formula

${\displaystyle{\displaystyle n}}$

xml-id

C2.S6.XMD20.m1jdec

0 references

Q11036

Defining formula

${\displaystyle{\displaystyle\delta_{n}(x)}}$

xml-id

C2.S6.XMD25.m1cdec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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