DLMF:15.9.E10 (Q5100): Difference between revisions

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Revision as of 14:09, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 14:09, 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
			base of natural logarithm
		Property / Symbols used: base of natural logarithm / rank
			Normal rank
		Property / Symbols used: base of natural logarithm / qualifier
			Defining formula: ${\displaystyle{\displaystyle\mathrm{e}}}$ \expe
		Property / Symbols used: base of natural logarithm / qualifier
			xml-id: C4.S2.E11.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.m5addec
		Property / Symbols used
			imaginary unit
		Property / Symbols used: imaginary unit / rank
			Normal rank
		Property / Symbols used: imaginary unit / qualifier
			Defining formula: ${\displaystyle{\displaystyle\mathrm{i}}}$ \iunit
		Property / Symbols used: imaginary unit / qualifier
			xml-id: C1.S9.E1.m2aadec
		Property / Symbols used
			Q11649
		Property / Symbols used: Q11649 / rank
			Normal rank
		Property / Symbols used: Q11649 / qualifier
			Defining formula: ${\displaystyle{\displaystyle x}}$ x
		Property / Symbols used: Q11649 / qualifier
			xml-id: C15.S1.XMD1.m1hdec
		Property / Symbols used
			Q11650
		Property / Symbols used: Q11650 / rank
			Normal rank
		Property / Symbols used: Q11650 / qualifier
			Defining formula: ${\displaystyle{\displaystyle n}}$ n
		Property / Symbols used: Q11650 / qualifier
			xml-id: C15.S1.XMD10.m1idec

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Latest revision as of 14:09, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:15.9.E10	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle P^{(\lambda)}_{n}\left(x;\phi\right)=\frac{{\left(2\lambda\right)_{n}}}{n!}e^{n\mathrm{i}\phi}F\left({-n,\lambda+\mathrm{i}x\atop 2\lambda};1-e^{-2\mathrm{i}\phi}\right).}}$

0 references

DLMF id

DLMF:15.9.E10

0 references

Symbols used

$$={{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$ Gauss’ hypergeometric function

Defining formula

${\displaystyle{\displaystyle F\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)}}$

xml-id

C15.S2.E1.m2aidec

0 references

Q11664

Defining formula

${\displaystyle{\displaystyle P^{(\NVar{\lambda})}_{\NVar{n}}\left(\NVar{x};\NVar{\phi}\right)}}$

xml-id

C18.S19.Px3.p1.m2adec

0 references

Q10759

Defining formula

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

xml-id

C5.S2.SS3.m1addec

0 references

base of natural logarithm

Defining formula

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

xml-id

C4.S2.E11.m2aadec

0 references

Q10755

Defining formula

${\displaystyle{\displaystyle!}}$

xml-id

introduction.Sx4.p1.t1.r15.m5addec

0 references

imaginary unit

Defining formula

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

xml-id

C1.S9.E1.m2aadec

0 references

Q11649

Defining formula

${\displaystyle{\displaystyle x}}$

xml-id

C15.S1.XMD1.m1hdec

0 references

Q11650

Defining formula

${\displaystyle{\displaystyle n}}$

xml-id

C15.S1.XMD10.m1idec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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