DLMF:2.10.E2 (Q989)

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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},}}

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DLMF:2.10.E2

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Defining formula

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

C24.S2.SS1.m1aadec

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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2adec

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Defining formula

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

C1.S4.SS4.m1aadec

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base of natural logarithm

Defining formula

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

C4.S2.E11.m2adec

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Defining formula

{\displaystyle{\displaystyle!}}

introduction.Sx4.p1.t1.r15.m5aadec

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Defining formula

{\displaystyle{\displaystyle\Im}}

C1.S9.E2.m2adec

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Defining formula

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

C1.S9.E1.m2adec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3aadec

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Sitelinks

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