DLMF:24.4.E24 (Q7437): Difference between revisions

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Revision as of 18:12, 30 December 2019 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 01:28, 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
			Q11288
		Property / Symbols used: Q11288 / rank
			Normal rank
		Property / Symbols used: Q11288 / qualifier
			Defining formula: ${\displaystyle{\displaystyle B_{\NVar{n}}\left(\NVar{x}\right)}}$ \BernoullipolyB{\NVar{n}}@{\NVar{x}}
		Property / Symbols used: Q11288 / qualifier
			xml-id: C24.S2.SS1.m2akdec
		Property / Symbols used
			Q10754
		Property / Symbols used: Q10754 / rank
			Normal rank
		Property / Symbols used: Q10754 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}$ \binom{\NVar{m}}{\NVar{n}}
		Property / Symbols used: Q10754 / qualifier
			xml-id: C1.S2.SS1.m1agdec
		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.m2adec
		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
			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.m2adec
		Property / Symbols used
			Q12116
		Property / Symbols used: Q12116 / rank
			Normal rank
		Property / Symbols used: Q12116 / qualifier
			Defining formula: ${\displaystyle{\displaystyle j}}$ j
		Property / Symbols used: Q12116 / qualifier
			xml-id: C24.S1.XMD1.m1adec
		Property / Symbols used
			Q12113
		Property / Symbols used: Q12113 / rank
			Normal rank
		Property / Symbols used: Q12113 / qualifier
			Defining formula: ${\displaystyle{\displaystyle k}}$ k
		Property / Symbols used: Q12113 / qualifier
			xml-id: C24.S1.XMD2.m1ndec
		Property / Symbols used
			Q12115
		Property / Symbols used: Q12115 / rank
			Normal rank
		Property / Symbols used: Q12115 / qualifier
			Defining formula: ${\displaystyle{\displaystyle m}}$ m
		Property / Symbols used: Q12115 / qualifier
			xml-id: C24.S1.XMD4.m1hdec
		Property / Symbols used
			Q12110
		Property / Symbols used: Q12110 / rank
			Normal rank
		Property / Symbols used: Q12110 / qualifier
			Defining formula: ${\displaystyle{\displaystyle n}}$ n
		Property / Symbols used: Q12110 / qualifier
			xml-id: C24.S1.XMD5.m1wdec
		Property / Symbols used
			Q12112
		Property / Symbols used: Q12112 / rank
			Normal rank
		Property / Symbols used: Q12112 / qualifier
			Defining formula: ${\displaystyle{\displaystyle x}}$ x
		Property / Symbols used: Q12112 / qualifier
			xml-id: C24.S1.XMD7.m1odec

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Latest revision as of 01:28, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:24.4.E24	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle B_{n}\left(mx\right)=m^{n}B_{n}\left(x\right)+n\sum_{k=1}^{n}\sum_{j=0}^{k-1}(-1)^{j}{n\choose k}\*\left(\sum_{r=1}^{m-1}\frac{e^{2\pi i(k-j)r/m}}{(1-e^{2\pi ir/m})^{n}}\right)(j+mx)^{n-1},}}$

0 references

DLMF id

DLMF:24.4.E24

0 references

constraint

${\displaystyle{\displaystyle m=2,3,\dots}}$

0 references

Symbols used

Q11288

Defining formula

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

xml-id

C24.S2.SS1.m2akdec

0 references

Q10754

Defining formula

${\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}$

xml-id

C1.S2.SS1.m1agdec

0 references

the ratio of the circumference of a circle to its diameter

Defining formula

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

xml-id

C3.S12.E1.m2adec

0 references

base of natural logarithm

Defining formula

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

xml-id

C4.S2.E11.m2adec

0 references

imaginary unit

Defining formula

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

xml-id

C1.S9.E1.m2adec

0 references

Q12116

Defining formula

${\displaystyle{\displaystyle j}}$

xml-id

C24.S1.XMD1.m1adec

0 references

Q12113

Defining formula

${\displaystyle{\displaystyle k}}$

xml-id

C24.S1.XMD2.m1ndec

0 references

Q12115

Defining formula

${\displaystyle{\displaystyle m}}$

xml-id

C24.S1.XMD4.m1hdec

0 references

Q12110

Defining formula

${\displaystyle{\displaystyle n}}$

xml-id

C24.S1.XMD5.m1wdec

0 references

Q12112

Defining formula

${\displaystyle{\displaystyle x}}$

xml-id

C24.S1.XMD7.m1odec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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