DLMF:12.5.E6 (Q4120): Difference between revisions

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Revision as of 15:10, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 15:10, 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
			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
			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.m3aedec
		Property / Symbols used
			Q11320
		Property / Symbols used: Q11320 / rank
			Normal rank
		Property / Symbols used: Q11320 / qualifier
			Defining formula: ${\displaystyle{\displaystyle U\left(\NVar{a},\NVar{z}\right)}}$ \paraU@{\NVar{a}}{\NVar{z}}
		Property / Symbols used: Q11320 / qualifier
			xml-id: C12.S2.SS1.p1.m1aedec
		Property / Symbols used
			Q10817
		Property / Symbols used: Q10817 / rank
			Normal rank
		Property / Symbols used: Q10817 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\operatorname{ph}}}$ \phase
		Property / Symbols used: Q10817 / qualifier
			xml-id: C1.S9.E7.m1acdec
		Property / Symbols used
			Q11513
		Property / Symbols used: Q11513 / rank
			Normal rank
		Property / Symbols used: Q11513 / qualifier
			Defining formula: ${\displaystyle{\displaystyle z}}$ z
		Property / Symbols used: Q11513 / qualifier
			xml-id: C12.S1.XMD3.m1edec
		Property / Symbols used
			Q11516
		Property / Symbols used: Q11516 / rank
			Normal rank
		Property / Symbols used: Q11516 / qualifier
			Defining formula: ${\displaystyle{\displaystyle a}}$ a
		Property / Symbols used: Q11516 / qualifier
			xml-id: C12.S1.XMD6.m1edec

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Latest revision as of 15:10, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:12.5.E6	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle U\left(a,z\right)=\frac{e^{\frac{1}{4}z^{2}}}{i\sqrt{2\pi}}\int_{c-i\infty}^{c+i\infty}e^{-zt+\frac{1}{2}t^{2}}t^{-a-\frac{1}{2}}\mathrm{d}t,}}$

0 references

DLMF id

DLMF:12.5.E6

0 references

constraint

${\displaystyle{\displaystyle-\tfrac{1}{2}\pi<\operatorname{ph}t<\tfrac{1}{2}\pi}}$

0 references

${\displaystyle{\displaystyle-\tfrac{1}{2}\pi<\operatorname{ph}t<\tfrac{1}{2}\pi}}$

0 references

${\displaystyle{\displaystyle c>0}}$

0 references

Symbols used

the ratio of the circumference of a circle to its diameter

Defining formula

${\displaystyle{\displaystyle\pi}}$

xml-id

C3.S12.E1.m2addec

0 references

Q10770

Defining formula

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

xml-id

C1.S4.SS4.m1aedec

0 references

base of natural logarithm

Defining formula

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

xml-id

C4.S2.E11.m2aedec

0 references

imaginary unit

Defining formula

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

xml-id

C1.S9.E1.m2aadec

0 references

Q10771

Defining formula

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

xml-id

C1.S4.SS4.m3aedec

0 references

Q11320

Defining formula

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

xml-id

C12.S2.SS1.p1.m1aedec

0 references

Q10817

Defining formula

${\displaystyle{\displaystyle\operatorname{ph}}}$

xml-id

C1.S9.E7.m1acdec

0 references

Q11513

Defining formula

${\displaystyle{\displaystyle z}}$

xml-id

C12.S1.XMD3.m1edec

0 references

Q11516

Defining formula

${\displaystyle{\displaystyle a}}$

xml-id

C12.S1.XMD6.m1edec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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