DLMF:18.28.E17 (Q5992): Difference between revisions

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Revision as of 13:24, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 13:24, 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.m1edec
		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.m1ldec

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Latest revision as of 13:24, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:18.28.E17	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle\frac{1}{2\pi}\int_{0}^{\pi}H_{n}\left(\cos\theta\,|\,q\right)H_{m}\left(\cos\theta\,|\,q\right){\left|\left(e^{2\mathrm{i}\theta};q\right)_{\infty}\right|^{2}}\mathrm{d}\theta=\frac{\delta_{n,m}}{\left(q^{n+1};q\right)_{\infty}}.}}$

0 references

DLMF id

DLMF:18.28.E17

0 references

Symbols used

Q10768

Defining formula

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

xml-id

introduction.Sx4.p1.t1.r4.m5aedec

0 references

the ratio of the circumference of a circle to its diameter

Defining formula

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

xml-id

C3.S12.E1.m2acdec

0 references

continuous $$q$$ -Hermite polynomial

Defining formula

${\displaystyle{\displaystyle H_{\NVar{n}}\left(\NVar{x}\,|\,\NVar{q}\right)}}$

xml-id

C18.S28.E16.m2aadec

0 references

cosine function

Defining formula

${\displaystyle{\displaystyle\cos\NVar{z}}}$

xml-id

C4.S14.E2.m2ahdec

0 references

Q10770

Defining formula

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

xml-id

C1.S4.SS4.m1addec

0 references

base of natural logarithm

Defining formula

${\displaystyle{\displaystyle\mathrm{e}}}$

xml-id

C4.S2.E11.m2ahdec

0 references

imaginary unit

Defining formula

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

xml-id

C1.S9.E1.m2aidec

0 references

Q10771

Defining formula

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

xml-id

C1.S4.SS4.m3addec

0 references

Q11298

Defining formula

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

xml-id

C17.S2.SS1.p1.m2aldec

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.m1edec

0 references

Q11726

Defining formula

${\displaystyle{\displaystyle n}}$

xml-id

C18.S1.XMD6.m1ldec

0 references

 

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