DLMF:7.7.E10 (Q2380): Difference between revisions

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Revision as of 23:44, 1 January 2020 Admin (talk | contribs) (‎Changed an Item: Add constraint) ← Older edit		Latest revision as of 23:45, 1 January 2020 Admin (talk | contribs) (‎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.m1aidec
		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.m2aidec
		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.m3aidec
		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
			Q11312
		Property / Symbols used: Q11312 / rank
			Normal rank
		Property / Symbols used: Q11312 / qualifier
			Defining formula: ${\displaystyle{\displaystyle z}}$ z
		Property / Symbols used: Q11312 / qualifier
			xml-id: C7.S1.XMD2.m1ddec

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Latest revision as of 23:45, 1 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:7.7.E10	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle\mathrm{f}\left(z\right)=\frac{1}{\pi\sqrt{2}}\int_{0}^{\infty}\frac{e^{-\pi z^{2}t/2}}{\sqrt{t}(t^{2}+1)}\mathrm{d}t,}}$

0 references

DLMF id

DLMF:7.7.E10

0 references

constraint

${\displaystyle{\displaystyle|\operatorname{ph}z|\leq\frac{1}{4}\pi}}$

0 references

Symbols used

auxiliary function for Fresnel integrals

Defining formula

${\displaystyle{\displaystyle\mathrm{f}\left(\NVar{z}\right)}}$

xml-id

C7.S2.E10.m2adec

0 references

the ratio of the circumference of a circle to its diameter

Defining formula

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

xml-id

C3.S12.E1.m2aidec

0 references

Q10770

Defining formula

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

xml-id

C1.S4.SS4.m1aidec

0 references

base of natural logarithm

Defining formula

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

xml-id

C4.S2.E11.m2aidec

0 references

Q10771

Defining formula

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

xml-id

C1.S4.SS4.m3aidec

0 references

Q10817

Defining formula

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

xml-id

C1.S9.E7.m1acdec

0 references

Q11312

Defining formula

${\displaystyle{\displaystyle z}}$

xml-id

C7.S1.XMD2.m1ddec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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