DLMF:13.11.E1 (Q4476): Difference between revisions

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Revision as of 16:02, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 16:03, 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
			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.m2adec
		Property / Symbols used
			Q10755
		Property / Symbols used: Q10755 / rank
			Normal rank
		Property / Symbols used: Q10755 / qualifier
			Defining formula: ${\displaystyle{\displaystyle!}}$ !
		Property / Symbols used: Q10755 / qualifier
			xml-id: introduction.Sx4.p1.t1.r15.m5adec
		Property / Symbols used
			Q11558
		Property / Symbols used: Q11558 / rank
			Normal rank
		Property / Symbols used: Q11558 / qualifier
			Defining formula: ${\displaystyle{\displaystyle s}}$ s
		Property / Symbols used: Q11558 / qualifier
			xml-id: C13.S1.XMD3.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.m1dec
		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

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Latest revision as of 16:03, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:13.11.E1	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle M\left(a,b,z\right)=\Gamma\left(a-\tfrac{1}{2}\right)e^{\frac{1}{2}z}\left(\tfrac{1}{4}z\right)^{\frac{1}{2}-a}\*\sum_{s=0}^{\infty}\frac{{\left(2a-1\right)_{s}}{\left(2a-b\right)_{s}}}{{\left(b\right)_{s}}s!}\*\left(a-\tfrac{1}{2}+s\right)\*I_{a-\frac{1}{2}+s}\left(\tfrac{1}{2}z\right),}}$

0 references

DLMF id

DLMF:13.11.E1

0 references

constraint

${\displaystyle{\displaystyle a+\frac{1}{2},b\neq 0,-1,-2,\dots}}$

0 references

Symbols used

gamma function

Defining formula

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

xml-id

C5.S2.E1.m2adec

0 references

$$={{}_{1}F_{1}}\left(\NVar{a};\NVar{b};\NVar{z}\right)$$ Kummer confluent hypergeometric function

Defining formula

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

xml-id

C13.S2.E2.m2adec

0 references

Q10759

Defining formula

${\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}$

xml-id

C5.S2.SS3.m1adec

0 references

base of natural logarithm

Defining formula

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

xml-id

C4.S2.E11.m2adec

0 references

Q10755

Defining formula

${\displaystyle{\displaystyle!}}$

xml-id

introduction.Sx4.p1.t1.r15.m5adec

0 references

Q11558

Defining formula

${\displaystyle{\displaystyle s}}$

xml-id

C13.S1.XMD3.m1dec

0 references

Q11557

Defining formula

${\displaystyle{\displaystyle z}}$

xml-id

C13.S1.XMD6.m1dec

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

 

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