DLMF:18.18.E28 (Q5818): Difference between revisions

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Revision as of 01:26, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 01:27, 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
			exponential function
		Property / Symbols used: exponential function / rank
			Normal rank
		Property / Symbols used: exponential function / qualifier
			Defining formula: ${\displaystyle{\displaystyle\exp\NVar{z}}}$ \exp@@{\NVar{z}}
		Property / Symbols used: exponential function / qualifier
			xml-id: C4.S2.E19.m2aadec
		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.m5aodec
		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.m1bdec
		Property / Symbols used
			Q11750
		Property / Symbols used: Q11750 / rank
			Normal rank
		Property / Symbols used: Q11750 / qualifier
			Defining formula: ${\displaystyle{\displaystyle z}}$ z
		Property / Symbols used: Q11750 / qualifier
			xml-id: C18.S1.XMD2.m1bdec
		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.m1aadec
		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.m1wdec

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Latest revision as of 01:27, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:18.18.E28	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle\sum_{n=0}^{\infty}\frac{H_{n}\left(x\right)H_{n}\left(y\right)}{2^{n}n!}z^{n}=(1-z^{2})^{-\frac{1}{2}}\exp\left(\frac{2xyz-(x^{2}+y^{2})z^{2}}{1-z^{2}}\right),}}$

0 references

DLMF id

DLMF:18.18.E28

0 references

constraint

${\displaystyle{\displaystyle|z|<1}}$

0 references

Symbols used

Q10922

Defining formula

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

xml-id

C18.S3.T1.t1.r13.m2afdec

0 references

exponential function

Defining formula

${\displaystyle{\displaystyle\exp\NVar{z}}}$

xml-id

C4.S2.E19.m2aadec

0 references

Q10755

Defining formula

${\displaystyle{\displaystyle!}}$

xml-id

introduction.Sx4.p1.t1.r15.m5aodec

0 references

Q11743

Defining formula

${\displaystyle{\displaystyle y}}$

xml-id

C18.S1.XMD1.m1bdec

0 references

Q11750

Defining formula

${\displaystyle{\displaystyle z}}$

xml-id

C18.S1.XMD2.m1bdec

0 references

Q11726

Defining formula

${\displaystyle{\displaystyle n}}$

xml-id

C18.S1.XMD6.m1aadec

0 references

Q11727

Defining formula

${\displaystyle{\displaystyle x}}$

xml-id

C18.S2.XMD3.m1wdec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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