DLMF:13.10.E8 (Q4467): Difference between revisions

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Revision as of 16:01, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 16:01, 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
			modified Bessel function of the first kind
		Property / Symbols used: modified Bessel function of the first kind / rank
			Normal rank
		Property / Symbols used: modified Bessel function of the first kind / qualifier
			Defining formula: ${\displaystyle{\displaystyle I_{\NVar{\nu}}\left(\NVar{z}\right)}}$ \modBesselI{\NVar{\nu}}@{\NVar{z}}
		Property / Symbols used: modified Bessel function of the first kind / qualifier
			xml-id: C10.S25.E2.m2adec
		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.m1aedec
		Property / Symbols used
			Q11580
		Property / Symbols used: Q11580 / rank
			Normal rank
		Property / Symbols used: Q11580 / qualifier
			Defining formula: ${\displaystyle{\displaystyle y}}$ y
		Property / Symbols used: Q11580 / qualifier
			xml-id: C13.S1.XMD5.m1dec
		Property / Symbols used
			Q11557
		Property / Symbols used: Q11557 / rank
			Normal rank
		Property / Symbols used: Q11557 / qualifier
			Defining formula: ${\displaystyle{\displaystyle z}}$ z
		Property / Symbols used: Q11557 / qualifier
			xml-id: C13.S1.XMD6.m1fdec
		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.m3agdec

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Latest revision as of 16:01, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:13.10.E8	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle\frac{1}{2\pi\mathrm{i}}\int_{-\infty}^{(0+)}e^{tz}t^{-a}{\mathbf{M}}\left(a,b,\ifrac{y}{t}\right)\mathrm{d}t=\frac{1}{\Gamma\left(a\right)}z^{\frac{1}{2}(2a-b-1)}y^{\frac{1}{2}(1-b)}I_{b-1}\left(2\sqrt{zy}\right),}}$

0 references

DLMF id

DLMF:13.10.E8

0 references

constraint

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

0 references

Symbols used

gamma function

Defining formula

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

xml-id

C5.S2.E1.m2addec

0 references

Olver’s confluent hypergeometric function

Defining formula

${\displaystyle{\displaystyle{\mathbf{M}}\left(\NVar{a},\NVar{b},\NVar{z}\right)}}$

xml-id

C13.S2.E3.m2aedec

0 references

the ratio of the circumference of a circle to its diameter

Defining formula

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

xml-id

C3.S12.E1.m2aadec

0 references

Q10770

Defining formula

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

xml-id

C1.S4.SS4.m1agdec

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.m2adec

0 references

modified Bessel function of the first kind

Defining formula

${\displaystyle{\displaystyle I_{\NVar{\nu}}\left(\NVar{z}\right)}}$

xml-id

C10.S25.E2.m2adec

0 references

Q10811

Defining formula

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

xml-id

C1.S9.E2.m1aedec

0 references

Q11580

Defining formula

${\displaystyle{\displaystyle y}}$

xml-id

C13.S1.XMD5.m1dec

0 references

Q11557

Defining formula

${\displaystyle{\displaystyle z}}$

xml-id

C13.S1.XMD6.m1fdec

0 references

Q10771

Defining formula

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

xml-id

C1.S4.SS4.m3agdec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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