DLMF:10.22.E12 (Q3386): Difference between revisions

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Revision as of 15:49, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 15:49, 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
			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.m1akdec
		Property / Symbols used
			psi (or digamma) function
		Property / Symbols used: psi (or digamma) function / rank
			Normal rank
		Property / Symbols used: psi (or digamma) function / qualifier
			Defining formula: ${\displaystyle{\displaystyle\psi\left(\NVar{z}\right)}}$ \digamma@{\NVar{z}}
		Property / Symbols used: psi (or digamma) function / qualifier
			xml-id: C5.S2.E2.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.m3akdec
		Property / Symbols used
			Q11428
		Property / Symbols used: Q11428 / rank
			Normal rank
		Property / Symbols used: Q11428 / qualifier
			Defining formula: ${\displaystyle{\displaystyle k}}$ k
		Property / Symbols used: Q11428 / qualifier
			xml-id: C10.S1.XMD3.m1ddec
		Property / Symbols used
			Q11435
		Property / Symbols used: Q11435 / rank
			Normal rank
		Property / Symbols used: Q11435 / qualifier
			Defining formula: ${\displaystyle{\displaystyle x}}$ x
		Property / Symbols used: Q11435 / qualifier
			xml-id: C10.S1.XMD4.m1ddec

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Latest revision as of 15:49, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:10.22.E12	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle x\int_{0}^{x}\frac{1-J_{0}\left(t\right)}{t}\mathrm{d}t=2\sum_{k=0}^{\infty}(2k+3)(\psi\left(k+2\right)-\psi\left(1\right))J_{2k+3}\left(x\right)=x-2J_{1}\left(x\right)+2\sum_{k=0}^{\infty}(2k+5)\*(\psi\left(k+3\right)-\psi\left(1\right)-1)J_{2k+5}\left(x\right),}}$

0 references

DLMF id

DLMF:10.22.E12

0 references

Symbols used

Bessel function of the first kind

Defining formula

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

xml-id

C10.S2.E2.m2addec

0 references

Q10770

Defining formula

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

xml-id

C1.S4.SS4.m1akdec

0 references

psi (or digamma) function

Defining formula

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

xml-id

C5.S2.E2.m2aadec

0 references

Q10771

Defining formula

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

xml-id

C1.S4.SS4.m3akdec

0 references

Q11428

Defining formula

${\displaystyle{\displaystyle k}}$

xml-id

C10.S1.XMD3.m1ddec

0 references

Q11435

Defining formula

${\displaystyle{\displaystyle x}}$

xml-id

C10.S1.XMD4.m1ddec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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