DLMF:2.10.E2 (Q989): Difference between revisions

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Revision as of 17:33, 1 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 17:33, 1 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint
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		Property / Symbols used
			Q10901
		Property / Symbols used: Q10901 / rank
			Normal rank
		Property / Symbols used: Q10901 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\Im}}$ \imagpart@@
		Property / Symbols used: Q10901 / qualifier
			xml-id: C1.S9.E2.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
			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.m3aadec
		Property / Symbols used
			Q11111
		Property / Symbols used: Q11111 / rank
			Normal rank
		Property / Symbols used: Q11111 / qualifier
			Defining formula: ${\displaystyle{\displaystyle a}}$ a
		Property / Symbols used: Q11111 / qualifier
			xml-id: C2.S10.XMD1.m1adec
		Property / Symbols used
			Q11112
		Property / Symbols used: Q11112 / rank
			Normal rank
		Property / Symbols used: Q11112 / qualifier
			Defining formula: ${\displaystyle{\displaystyle m}}$ m
		Property / Symbols used: Q11112 / qualifier
			xml-id: C2.S10.XMD2.m1adec
		Property / Symbols used
			Q11113
		Property / Symbols used: Q11113 / rank
			Normal rank
		Property / Symbols used: Q11113 / qualifier
			Defining formula: ${\displaystyle{\displaystyle n}}$ n
		Property / Symbols used: Q11113 / qualifier
			xml-id: C2.S10.XMD3.m1adec
		Property / Symbols used
			Q11114
		Property / Symbols used: Q11114 / rank
			Normal rank
		Property / Symbols used: Q11114 / qualifier
			Defining formula: ${\displaystyle{\displaystyle f(x)}}$ f(x)
		Property / Symbols used: Q11114 / qualifier
			xml-id: C2.S10.XMD4.m1adec

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Latest revision as of 17:33, 1 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:2.10.E2	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle\sum_{j=a}^{n}f(j)=\int_{a}^{n}f(x)\mathrm{d}x+\tfrac{1}{2}f(a)+\tfrac{1}{2}f(n)-2\int_{0}^{\infty}\frac{\Im(f(a+iy))}{e^{2\pi y}-1}\mathrm{d}y+\sum_{s=1}^{m}\frac{B_{2s}}{(2s)!}f^{(2s-1)}(n)+2\frac{(-1)^{m}}{(2m)!}\int_{0}^{\infty}\Im(f^{(2m)}(n+i\vartheta_{n}y))\frac{y^{2m}\mathrm{d}y}{e^{2\pi y}-1},}}$

0 references

DLMF id

DLMF:2.10.E2

0 references

Symbols used

Q11109

Defining formula

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

xml-id

C24.S2.SS1.m1aadec

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

Q10770

Defining formula

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

xml-id

C1.S4.SS4.m1aadec

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.m5aadec

0 references

Q10901

Defining formula

${\displaystyle{\displaystyle\Im}}$

xml-id

C1.S9.E2.m2adec

0 references

imaginary unit

Defining formula

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

xml-id

C1.S9.E1.m2adec

0 references

Q10771

Defining formula

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

xml-id

C1.S4.SS4.m3aadec

0 references

Q11111

Defining formula

${\displaystyle{\displaystyle a}}$

xml-id

C2.S10.XMD1.m1adec

0 references

Q11112

Defining formula

${\displaystyle{\displaystyle m}}$

xml-id

C2.S10.XMD2.m1adec

0 references

Q11113

Defining formula

${\displaystyle{\displaystyle n}}$

xml-id

C2.S10.XMD3.m1adec

0 references

Q11114

Defining formula

${\displaystyle{\displaystyle f(x)}}$

xml-id

C2.S10.XMD4.m1adec

0 references

 

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