DLMF:8.19.E27 (Q2713): Difference between revisions

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Revision as of 14:13, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 14:13, 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
			Q10770
		Property / Symbols used: Q10770 / rank
			Normal rank
		Property / Symbols used: Q10770 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$ \diff{\NVar{x}}
		Property / Symbols used: Q10770 / qualifier
			xml-id: C1.S4.SS4.m1ahdec
		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.m2apdec
		Property / Symbols used
			generalized exponential integral
		Property / Symbols used: generalized exponential integral / rank
			Normal rank
		Property / Symbols used: generalized exponential integral / qualifier
			Defining formula: ${\displaystyle{\displaystyle E_{\NVar{p}}\left(\NVar{z}\right)}}$ \genexpintE{\NVar{p}}@{\NVar{z}}
		Property / Symbols used: generalized exponential integral / qualifier
			xml-id: C8.S19.E1.m2aaedec
		Property / Symbols used
			Q10771
		Property / Symbols used: Q10771 / rank
			Normal rank
		Property / Symbols used: Q10771 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\int}}$ \int
		Property / Symbols used: Q10771 / qualifier
			xml-id: C1.S4.SS4.m3ahdec
		Property / Symbols used
			Q11377
		Property / Symbols used: Q11377 / rank
			Normal rank
		Property / Symbols used: Q11377 / qualifier
			Defining formula: ${\displaystyle{\displaystyle p}}$ p
		Property / Symbols used: Q11377 / qualifier
			xml-id: C8.S1.XMD4.m1rdec
		Property / Symbols used
			Q11379
		Property / Symbols used: Q11379 / rank
			Normal rank
		Property / Symbols used: Q11379 / qualifier
			Defining formula: ${\displaystyle{\displaystyle L(p)}}$ L(p)
		Property / Symbols used: Q11379 / qualifier
			xml-id: C8.S19.XMD2.m1adec

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Latest revision as of 14:13, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:8.19.E27	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle L(p)=\int_{0}^{\infty}e^{-t}E_{p}\left(t\right)\mathrm{d}t=\frac{1}{2p}F\left(1,1;1+p;\tfrac{1}{2}\right),}}$

0 references

DLMF id

DLMF:8.19.E27

0 references

constraint

${\displaystyle{\displaystyle p>0}}$

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.m2aadec

0 references

Q10770

Defining formula

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

xml-id

C1.S4.SS4.m1ahdec

0 references

base of natural logarithm

Defining formula

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

xml-id

C4.S2.E11.m2apdec

0 references

generalized exponential integral

Defining formula

${\displaystyle{\displaystyle E_{\NVar{p}}\left(\NVar{z}\right)}}$

xml-id

C8.S19.E1.m2aaedec

0 references

Q10771

Defining formula

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

xml-id

C1.S4.SS4.m3ahdec

0 references

Q11377

Defining formula

${\displaystyle{\displaystyle p}}$

xml-id

C8.S1.XMD4.m1rdec

0 references

Q11379

Defining formula

${\displaystyle{\displaystyle L(p)}}$

xml-id

C8.S19.XMD2.m1adec

0 references

 

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