DLMF:18.27.E16 (Q5967): Difference between revisions

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Revision as of 01:50, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 01:50, 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
			Q11728
		Property / Symbols used: Q11728 / rank
			Normal rank
		Property / Symbols used: Q11728 / qualifier
			Defining formula: ${\displaystyle{\displaystyle q}}$ q
		Property / Symbols used: Q11728 / qualifier
			xml-id: C18.S1.XMD3.m1ndec
		Property / Symbols used
			Q11730
		Property / Symbols used: Q11730 / rank
			Normal rank
		Property / Symbols used: Q11730 / qualifier
			Defining formula: ${\displaystyle{\displaystyle m}}$ m
		Property / Symbols used: Q11730 / qualifier
			xml-id: C18.S1.XMD5.m1cdec
		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.m1kdec
		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.m1kdec
		Property / Symbols used
			DLMF:18.2.E5
		Property / Symbols used: DLMF:18.2.E5 / rank
			Normal rank
		Property / Symbols used: DLMF:18.2.E5 / qualifier
			Defining formula: ${\displaystyle{\displaystyle h_{n}}}$ h_{n}
		Property / Symbols used: DLMF:18.2.E5 / qualifier
			xml-id: C18.S2.XMD4.m1cdec

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Latest revision as of 01:50, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:18.27.E16	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle\int_{0}^{\infty}L^{(\alpha)}_{n}\left(x;q\right)L^{(\alpha)}_{m}\left(x;q\right)\frac{x^{\alpha}}{\left(-x;q\right)_{\infty}}\mathrm{d}x=\frac{\left(q^{\alpha+1};q\right)_{n}}{\left(q;q\right)_{n}q^{n}}h_{0}^{(1)}\delta_{n,m},}}$

0 references

DLMF id

DLMF:18.27.E16

0 references

constraint

${\displaystyle{\displaystyle\alpha>-1}}$

0 references

Symbols used

Q10768

Defining formula

${\displaystyle{\displaystyle\delta_{\NVar{j},\NVar{k}}}}$

xml-id

introduction.Sx4.p1.t1.r4.m5acdec

0 references

Q10770

Defining formula

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

xml-id

C1.S4.SS4.m1adec

0 references

Q10771

Defining formula

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

xml-id

C1.S4.SS4.m3adec

0 references

$$q$$ -Laguerre polynomial

Defining formula

${\displaystyle{\displaystyle L^{(\NVar{\alpha})}_{\NVar{n}}\left(\NVar{x};\NVar{q}\right)}}$

xml-id

C18.S27.E15.m2aadec

0 references

Q11298

Defining formula

${\displaystyle{\displaystyle\left(\NVar{a};\NVar{q}\right)_{\NVar{n}}}}$

xml-id

C17.S2.SS1.p1.m2abdec

0 references

Q11728

Defining formula

${\displaystyle{\displaystyle q}}$

xml-id

C18.S1.XMD3.m1ndec

0 references

Q11730

Defining formula

${\displaystyle{\displaystyle m}}$

xml-id

C18.S1.XMD5.m1cdec

0 references

Q11726

Defining formula

${\displaystyle{\displaystyle n}}$

xml-id

C18.S1.XMD6.m1kdec

0 references

Q11727

Defining formula

${\displaystyle{\displaystyle x}}$

xml-id

C18.S2.XMD3.m1kdec

0 references

DLMF:18.2.E5

Defining formula

${\displaystyle{\displaystyle h_{n}}}$

xml-id

C18.S2.XMD4.m1cdec

0 references

 

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