DLMF:8.6.E9 (Q2523): Difference between revisions

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Revision as of 13:43, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 13:44, 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
			the ratio of the circumference of a circle to its diameter
		Property / Symbols used: the ratio of the circumference of a circle to its diameter / rank
			Normal rank
		Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
			Defining formula: ${\displaystyle{\displaystyle\pi}}$ \cpi
		Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
			xml-id: C3.S12.E1.m2acdec
		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.m2ahdec
		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
			incomplete gamma function
		Property / Symbols used: incomplete gamma function / rank
			Normal rank
		Property / Symbols used: incomplete gamma function / qualifier
			Defining formula: ${\displaystyle{\displaystyle\Gamma\left(\NVar{a},\NVar{z}\right)}}$ \incGamma@{\NVar{a}}{\NVar{z}}
		Property / Symbols used: incomplete gamma function / qualifier
			xml-id: C8.S2.E2.m2addec
		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
			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.m1afdec
		Property / Symbols used
			Q11323
		Property / Symbols used: Q11323 / rank
			Normal rank
		Property / Symbols used: Q11323 / qualifier
			Defining formula: ${\displaystyle{\displaystyle z}}$ z
		Property / Symbols used: Q11323 / qualifier
			xml-id: C8.S1.XMD2.m1hdec
		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.m1hdec

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Latest revision as of 13:44, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:8.6.E9	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle\Gamma\left(-a,ze^{\pm\pi i}\right)=\frac{e^{z}e^{\mp\pi\mathrm{i}a}}{\Gamma\left(1+a\right)}\int_{0}^{\infty}\frac{t^{a}e^{-zt}}{t-1}\mathrm{d}t,}}$

0 references

DLMF id

DLMF:8.6.E9

0 references

constraint

${\displaystyle{\displaystyle\Re z>0}}$

0 references

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

0 references

Symbols used

gamma function

Defining formula

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

xml-id

C5.S2.E1.m2abdec

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

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.m2ahdec

0 references

imaginary unit

Defining formula

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

xml-id

C1.S9.E1.m2aadec

0 references

incomplete gamma function

Defining formula

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

xml-id

C8.S2.E2.m2addec

0 references

Q10771

Defining formula

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

xml-id

C1.S4.SS4.m3ahdec

0 references

Q10811

Defining formula

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

xml-id

C1.S9.E2.m1afdec

0 references

Q11323

Defining formula

${\displaystyle{\displaystyle z}}$

xml-id

C8.S1.XMD2.m1hdec

0 references

Q11324

Defining formula

${\displaystyle{\displaystyle a}}$

xml-id

C8.S1.XMD3.m1hdec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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