DLMF:25.11.E34 (Q7708): Difference between revisions

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Revision as of 13:44, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 13:44, 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
			Riemann zeta function
		Property / Symbols used: Riemann zeta function / rank
			Normal rank
		Property / Symbols used: Riemann zeta function / qualifier
			Defining formula: ${\displaystyle{\displaystyle\zeta\left(\NVar{s}\right)}}$ \Riemannzeta@{\NVar{s}}
		Property / Symbols used: Riemann zeta function / qualifier
			xml-id: C25.S2.E1.m2ahdec
		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
			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.m1aqdec
		Property / Symbols used
			Q12148
		Property / Symbols used: Q12148 / rank
			Normal rank
		Property / Symbols used: Q12148 / qualifier
			Defining formula: ${\displaystyle{\displaystyle n}}$ n
		Property / Symbols used: Q12148 / qualifier
			xml-id: C25.S1.XMD3.m1qdec
		Property / Symbols used
			Q12152
		Property / Symbols used: Q12152 / rank
			Normal rank
		Property / Symbols used: Q12152 / qualifier
			Defining formula: ${\displaystyle{\displaystyle x}}$ x
		Property / Symbols used: Q12152 / qualifier
			xml-id: C25.S1.XMD5.m1ndec
		Property / Symbols used
			Q12161
		Property / Symbols used: Q12161 / rank
			Normal rank
		Property / Symbols used: Q12161 / qualifier
			Defining formula: ${\displaystyle{\displaystyle a}}$ a
		Property / Symbols used: Q12161 / qualifier
			xml-id: C25.S1.XMD6.m1abdec

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Latest revision as of 13:44, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:25.11.E34	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle n\int_{0}^{a}\zeta'\left(1-n,x\right)\mathrm{d}x=\zeta'\left(-n,a\right)-\zeta'\left(-n\right)+\frac{B_{n+1}-B_{n+1}\left(a\right)}{n(n+1)},}}$

0 references

DLMF id

DLMF:25.11.E34

0 references

constraint

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

0 references

${\displaystyle{\displaystyle n=1,2,\dots}}$

0 references

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

0 references

Symbols used

Q11109

Defining formula

${\displaystyle{\displaystyle B_{\NVar{n}}}}$

xml-id

C24.S2.SS1.m1aidec

0 references

Q11288

Defining formula

${\displaystyle{\displaystyle B_{\NVar{n}}\left(\NVar{x}\right)}}$

xml-id

C24.S2.SS1.m2abdec

0 references

Hurwitz zeta function

Defining formula

${\displaystyle{\displaystyle\zeta\left(\NVar{s},\NVar{a}\right)}}$

xml-id

C25.S11.E1.m2aahdec

0 references

Riemann zeta function

Defining formula

${\displaystyle{\displaystyle\zeta\left(\NVar{s}\right)}}$

xml-id

C25.S2.E1.m2ahdec

0 references

Q10770

Defining formula

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

xml-id

C1.S4.SS4.m1amdec

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.m1aqdec

0 references

Q12148

Defining formula

${\displaystyle{\displaystyle n}}$

xml-id

C25.S1.XMD3.m1qdec

0 references

Q12152

Defining formula

${\displaystyle{\displaystyle x}}$

xml-id

C25.S1.XMD5.m1ndec

0 references

Q12161

Defining formula

${\displaystyle{\displaystyle a}}$

xml-id

C25.S1.XMD6.m1abdec

0 references

 

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