DLMF:18.17.E18 (Q5759): Difference between revisions

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Revision as of 15:48, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 15:48, 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
			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.m2abdec
		Property / Symbols used
			Q11475
		Property / Symbols used: Q11475 / rank
			Normal rank
		Property / Symbols used: Q11475 / qualifier
			Defining formula: ${\displaystyle{\displaystyle C^{(\NVar{\lambda})}_{\NVar{n}}\left(\NVar{x}\right)}}$ \ultrasphpoly{\NVar{\lambda}}{\NVar{n}}@{\NVar{x}}
		Property / Symbols used: Q11475 / qualifier
			xml-id: C18.S3.T1.t1.r3.m2addec
		Property / Symbols used
			Q11743
		Property / Symbols used: Q11743 / rank
			Normal rank
		Property / Symbols used: Q11743 / qualifier
			Defining formula: ${\displaystyle{\displaystyle y}}$ y
		Property / Symbols used: Q11743 / qualifier
			xml-id: C18.S1.XMD1.m1mdec
		Property / Symbols used
			Q11726
		Property / Symbols used: Q11726 / rank
			Normal rank
		Property / Symbols used: Q11726 / qualifier
			Defining formula: ${\displaystyle{\displaystyle n}}$ n
		Property / Symbols used: Q11726 / qualifier
			xml-id: C18.S1.XMD6.m1qdec
		Property / Symbols used
			Q11727
		Property / Symbols used: Q11727 / rank
			Normal rank
		Property / Symbols used: Q11727 / qualifier
			Defining formula: ${\displaystyle{\displaystyle x}}$ x
		Property / Symbols used: Q11727 / qualifier
			xml-id: C18.S2.XMD3.m1odec

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Latest revision as of 15:48, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:18.17.E18	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle\int_{0}^{1}(1-x^{2})^{\lambda-\frac{1}{2}}C^{(\lambda)}_{2n+1}\left(x\right)\sin\left(xy\right)\mathrm{d}x=\frac{(-1)^{n}\pi\Gamma\left(2n+2\lambda+1\right)J_{2n+\lambda+1}\left(y\right)}{(2n+1)!\Gamma\left(\lambda\right)(2y)^{\lambda}}.}}$

0 references

DLMF id

DLMF:18.17.E18

0 references

Symbols used

Bessel function of the first kind

Defining formula

${\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}$

xml-id

C10.S2.E2.m2aadec

0 references

gamma function

Defining formula

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

xml-id

C5.S2.E1.m2aidec

0 references

the ratio of the circumference of a circle to its diameter

Defining formula

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

xml-id

C3.S12.E1.m2aedec

0 references

Q10770

Defining formula

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

xml-id

C1.S4.SS4.m1aqdec

0 references

Q10755

Defining formula

${\displaystyle{\displaystyle!}}$

xml-id

introduction.Sx4.p1.t1.r15.m5acdec

0 references

Q10771

Defining formula

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

xml-id

C1.S4.SS4.m3aqdec

0 references

sine function

Defining formula

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

xml-id

C4.S14.E1.m2abdec

0 references

Q11475

Defining formula

${\displaystyle{\displaystyle C^{(\NVar{\lambda})}_{\NVar{n}}\left(\NVar{x}\right)}}$

xml-id

C18.S3.T1.t1.r3.m2addec

0 references

Q11743

Defining formula

${\displaystyle{\displaystyle y}}$

xml-id

C18.S1.XMD1.m1mdec

0 references

Q11726

Defining formula

${\displaystyle{\displaystyle n}}$

xml-id

C18.S1.XMD6.m1qdec

0 references

Q11727

Defining formula

${\displaystyle{\displaystyle x}}$

xml-id

C18.S2.XMD3.m1odec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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