DLMF:2.5.E42 (Q818): Difference between revisions

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Revision as of 12:28, 29 December 2019 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Created a new Item: Wikidata Toolkit example test item creation		Latest revision as of 17:07, 1 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint
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		Property / Symbols used
			gamma function
		Property / Symbols used: gamma function / rank
			Normal rank
		Property / Symbols used: gamma function / qualifier
			Defining formula: ${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$ \EulerGamma@{\NVar{z}}
		Property / Symbols used: gamma function / qualifier
			xml-id: C5.S2.E1.m2aedec
		Property / Symbols used
			Mellin transform
		Property / Symbols used: Mellin transform / rank
			Normal rank
		Property / Symbols used: Mellin transform / qualifier
			Defining formula: ${\displaystyle{\displaystyle\mathscr{M}\left(\NVar{f}\right)\left(\NVar{s}\right)}}$ \Mellintrans@{\NVar{f}}@{\NVar{s}}
		Property / Symbols used: Mellin transform / qualifier
			xml-id: C1.S14.E32.m2apdec
		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.m2ajdec
		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.m1amdec
		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.m2ajdec
		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.m3amdec
		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
			Q10960
		Property / Symbols used: Q10960 / rank
			Normal rank
		Property / Symbols used: Q10960 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\Residue}}$ \Residue
		Property / Symbols used: Q10960 / qualifier
			xml-id: C1.S10.SS3.p5.m4acdec
		Property / Symbols used
			Q11005
		Property / Symbols used: Q11005 / rank
			Normal rank
		Property / Symbols used: Q11005 / qualifier
			Defining formula: ${\displaystyle{\displaystyle h(x)}}$ h(x)
		Property / Symbols used: Q11005 / qualifier
			xml-id: C2.S5.XMD16.m1ndec
		Property / Symbols used
			Q11014
		Property / Symbols used: Q11014 / rank
			Normal rank
		Property / Symbols used: Q11014 / qualifier
			Defining formula: ${\displaystyle{\displaystyle I_{j}(x)}}$ I_{j}(x)
		Property / Symbols used: Q11014 / qualifier
			xml-id: C2.S5.XMD25.m1ddec
		Property / Symbols used
			Q11016
		Property / Symbols used: Q11016 / rank
			Normal rank
		Property / Symbols used: Q11016 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\rho}}$ \rho
		Property / Symbols used: Q11016 / qualifier
			xml-id: C2.S5.XMD27.m1adec

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Latest revision as of 17:07, 1 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:2.5.E42	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle I_{2}(x)=\sum_{\Re\beta_{0}\leq\Re z\leq 1}\Residue\left[-x^{-z}\Gamma\left(1-z\right)\mathscr{M}\mskip-3.0mu h_{2}\mskip 3.0mu \left(z\right)\right]+\frac{1}{2\pi i}\int_{\rho-i\infty}^{\rho+i\infty}x^{-z}\Gamma\left(1-z\right)\mathscr{M}\mskip-3.0mu h_{2}\mskip 3.0mu \left(z\right)\mathrm{d}z.}}$

0 references

DLMF id

DLMF:2.5.E42

0 references

Symbols used

gamma function

Defining formula

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

xml-id

C5.S2.E1.m2aedec

0 references

Mellin transform

Defining formula

${\displaystyle{\displaystyle\mathscr{M}\left(\NVar{f}\right)\left(\NVar{s}\right)}}$

xml-id

C1.S14.E32.m2apdec

0 references

the ratio of the circumference of a circle to its diameter

Defining formula

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

xml-id

C3.S12.E1.m2ajdec

0 references

Q10770

Defining formula

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

xml-id

C1.S4.SS4.m1amdec

0 references

imaginary unit

Defining formula

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

xml-id

C1.S9.E1.m2ajdec

0 references

Q10771

Defining formula

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

xml-id

C1.S4.SS4.m3amdec

0 references

Q10811

Defining formula

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

xml-id

C1.S9.E2.m1afdec

0 references

Q10960

Defining formula

${\displaystyle{\displaystyle\Residue}}$

xml-id

C1.S10.SS3.p5.m4acdec

0 references

Q11005

Defining formula

${\displaystyle{\displaystyle h(x)}}$

xml-id

C2.S5.XMD16.m1ndec

0 references

Q11014

Defining formula

${\displaystyle{\displaystyle I_{j}(x)}}$

xml-id

C2.S5.XMD25.m1ddec

0 references

Q11016

Defining formula

${\displaystyle{\displaystyle\rho}}$

xml-id

C2.S5.XMD27.m1adec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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