- ( v l × B ) ⋅ d l {\textstyle \
oint \left(\mathbf {v} \times \mathbf {B} \right)\cdot \mathrm {d} \mathbf {l} =\
oint \left(\mathbf {v} _{l}\times \mathbf...
- y))⋅Jy(ψ)dγ{\displaystyle \
oint _{\partial \Sigma }{\mathbf {F} (\mathbf {x} )\cdot \,\mathrm {d} \mathbf {\Gamma } }=\
oint _{\gamma }{\mathbf {F} ({\boldsymbol...
-
partial derivatives there, then ∮C(Ldx+Mdy)=∬D(∂M∂x−∂L∂y)dxdy{\displaystyle \
oint _{C}(L\,dx+M\,dy)=\iint _{D}\left({\frac {\partial M}{\partial x}}-{\frac...
-
interior of D, f(a)=12πi∮γf(z)z−adz.{\displaystyle f(a)={\frac {1}{2\pi i}}\
oint _{\gamma }{\frac {f(z)}{z-a}}\,dz.\,} The
proof of this
statement uses the...
- {3}{4z}}}}\\&=-i\
oint _{C}{\frac {4}{3z^{3}+10z+{\frac {3}{z}}}}\,dz\\&=-4i\
oint _{C}{\frac {dz}{3z^{3}+10z+{\frac {3}{z}}}}\\&=-4i\
oint _{C}{\frac...
-
structure only. The right-hand side is
sometimes written as ∮∂Ωω{\textstyle \
oint _{\partial \Omega }\omega } to
stress the fact that the (n−1){\displaystyle...
- i∮γ(vdx+udy){\displaystyle \
oint _{\gamma }f(z)\,dz=\
oint _{\gamma }(u+iv)(dx+i\,dy)=\
oint _{\gamma }(u\,dx-v\,dy)+i\
oint _{\gamma }(v\,dx+u\,dy)} By...
- −∮dSRes=∮δQTsurr≤0,{\displaystyle -\
oint dS_{\text{Res}}=\
oint {\frac {\delta Q}{T_{\text{surr}}}}\leq 0,}
where ∮dSRes{\displaystyle \
oint dS_{\text{Res}}} is the...
- \operatorname {Res} (f,c)={1 \over 2\pi i}\
oint _{\gamma }f(z)\,dz={1 \over 2\pi i}\sum _{n=-\infty }^{\infty }\
oint _{\gamma }a_{n}(z-c)^{n}\,dz=a_{-1}} using...
-
poles on C, then 12πi∮Cf′(z)f(z)dz=Z−P{\displaystyle {\frac {1}{2\pi i}}\
oint _{C}{f'(z) \over f(z)}\,dz=Z-P}
where Z and P
denote respectively the number...
