DLMF:8.19.E25 (Q2711): Difference between revisions

From DRMF

Jump to navigation Jump to search

← Older edit

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
(4 intermediate revisions by the same user not shown)
		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.m2aacdec
		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.m3afdec
		Property / Symbols used
			Q10811
		Property / Symbols used: Q10811 / rank
			Normal rank
		Property / Symbols used: Q10811 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\Re}}$ \realpart@@
		Property / Symbols used: Q10811 / qualifier
			xml-id: C1.S9.E2.m1addec
		Property / Symbols used
			Q11324
		Property / Symbols used: Q11324 / rank
			Normal rank
		Property / Symbols used: Q11324 / qualifier
			Defining formula: ${\displaystyle{\displaystyle a}}$ a
		Property / Symbols used: Q11324 / qualifier
			xml-id: C8.S1.XMD3.m1adec
		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.m1pdec

---

Latest revision as of 14:13, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:8.19.E25	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle\int_{0}^{\infty}e^{-at}t^{b-1}E_{p}\left(t\right)\mathrm{d}t=\frac{\Gamma\left(b\right)(1+a)^{-b}}{p+b-1}\*F\left(1,b;p+b;a/(1+a)\right),}}$

0 references

DLMF id

DLMF:8.19.E25

0 references

constraint

${\displaystyle{\displaystyle\Re a>-1}}$

0 references

${\displaystyle{\displaystyle\Re(p+b)>1}}$

0 references

Symbols used

gamma function

Defining formula

${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$

xml-id

C5.S2.E1.m2aedec

0 references

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

Defining formula

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

xml-id

C15.S2.E1.m2adec

0 references

Q10770

Defining formula

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

xml-id

C1.S4.SS4.m1afdec

0 references

base of natural logarithm

Defining formula

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

xml-id

C4.S2.E11.m2aodec

0 references

generalized exponential integral

Defining formula

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

xml-id

C8.S19.E1.m2aacdec

0 references

Q10771

Defining formula

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

xml-id

C1.S4.SS4.m3afdec

0 references

Q10811

Defining formula

${\displaystyle{\displaystyle\Re}}$

xml-id

C1.S9.E2.m1addec

0 references

Q11324

Defining formula

${\displaystyle{\displaystyle a}}$

xml-id

C8.S1.XMD3.m1adec

0 references

Q11377

Defining formula

${\displaystyle{\displaystyle p}}$

xml-id

C8.S1.XMD4.m1pdec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q2711&oldid=44737"