∮
∇∫
A
A′
a
a0
A1
a1
A2
a2
A3
a3
∇(a•b)
a*(∇b)
A_cap
∮[*(A_cap/2/π*∂(φ))′: ∂[∂(t): Bi(r - v*t,t)]•n′]
ag
ai
A_max
A_pie
Area
∂(Area)
∫[∂(Area): B(r,t)•n]
∬[∂(Area): (curl(v))_n]
∬[*∂(Area): (∇′Ei(r - v*t,t))n′]
∬[∂(Area): (∇′Ei(r - v*t,t))n′]
∬[∂(Area): ET(r)nh]
∫[∂(Area): ET(r,t)•nh]
∬[∂(Area): ∇F]
∮[•∂(Area),.over.S: B]
∫[∂(Area): ∂[∂(t): B(r,t))]
∬[∂(Area): ∇(v/cBi(r - v*t,t))]
∬[∂(Area): (∇′v)n′]
∬[∂(Area): (∇v)n]
A_sphere
A_surface_section
au
a(∇β)
B
∇B
b
B0
B0(r)
B0(r´,t´)
B0(r,t)
b1
b2
b3
Ba
b(∇a)
Ba(r)
bee
Bep
bep
Bi
Bi(r)
Bi(r´,t´)
Bi(r,t)
Bi(r,v)
Bi(r - vov*t,t)
Bi(r,v,t)
Bi(r - v*t,t)
Bpe
bpe
bpp
Brad
Brad(r)
B(r´,t´)
B(r´,t)
B(r,t)
B(r,t]
B(r,v,t)
B(r - v*t,t)
Bv
Bv(r)
C
c
c1
c2
c3
choose
choose(alpha,k)
choose( - m,n)
cos
cos(w1*t + P1)
cos(w2*t + P2)
cos(x)
∂(cos(θ))
cos(θ´)
cos(θ)
∫[∂(cos(θ)),0.to.π: ((1 - 3*cos(θ)^2/2))]
∫[∂(cos(θ)), - 1.to.1: ( - 1/8 - 1/4*cos(θ)^2 + 3/8*cos(θ)^4)]
∫[∂(cos(θ)), - 1.to.1: ( - 3/8 - 9/4*cos(θ)^2 + 15/8*cos(θ)^4)]
∫[∂(cos(θ)), - 1.to.1: k6]
cos(θf)
cos(π)
cos(φ)
cos(ω*t)
curl
curl(v)
d
d2
diff
diff(0.to.θf:  - 2*π*cos(θ))
E
∂(E)
E´
e
E0
E0(r)
E0(rs)
E0(r´,t´)
E0(r,t)
E0(r,v)
E0(r´v,t´)
E0(r - v*t,t´)
E0(r - v*t,t)
E0s
E0s(r)
E0s(rs)
E0s(r - v*t,t)
e1
e2
e3
Ea
EACH
Ea(r)
Ei
Ei´
Ei(r)
Ei(rs,vs)
Ei´(r´,t´)
Ei(r´,t´)
Ei(r´,t)
Ei(r,t)
Ei(r,v)
Ei´(r´,v´,t´)
Ei(r´,v´,t´)
Ei(r´v,t´)
Ei(r´v,t)
Ei(r,v,t)
Ei´(r - v*t,t)
Ei(r - v*t,t)
Ei(r - v*t,t)r´
Ei(r - v*t,t,θ´ = 0)
Eis
Eis(rs,vs)
Eis(r - v*t,t)
Ep(r´,t´)
E(r)
Erad
Erad(r)
E(rs,vs)
E(r´,t´)
E(r,t)
E(r,v)
E(r,v,t)
E(r - v*t,t)
Es
Es(rs,vs)
ET
∂(ET)
ET(r)
ET(rs,vs)
ET(r´,t´)
ET(r,t)
ET(r,v)
ET(r,v,t)
ET(r - v*t,t)
Ev
E_v_muchless_c
Ev(r)
F
F´
F0
F0(r´,t´)
f1
f2
F(2 - ,1 - )
F(2 - ,1 + )
F(2 + ,1 - )
F(2 + ,1 + )
F_B0
F_Ba
F_Bv
F_Coulomb
FE
F_E0
F_Ea
F_Ev
F_G
F_g
Fg1
Fg2
F_G_nonradial
F_G_nonradial(r,v)
F_G(r)
F_G_radial
F_G_radial(r,v)
F_gravity
F_G(r,v)
F_G_total
F_G_total(r,v)
F_I
Fi
Fi1
Fi2
Fi(2 + ,1 - )
Fi(2 + ,1 + )
Fij
Fi_neutral_dipoles
Fi_neutral_dipoles_nonNewton2nd
Fi_neutral_dipoles(r)
Fi(r´,t´)
F_Lienard_Wichert
F_Lienard_Wichert_electric_field_v_muchless_c
F_Lienard_Wichert_v_muchless_c
F_Lorentz_AmpInductn
FM
Fp
Fp(r´,t´)
F(q2,q1)
F_rad
F_real
F(r,O,φ,A1,w1,P1,t1,A2,w2,P2,t2,v)
F(r,O,φ,A1,w1,t)
F´(r´,t´)
F(r´,t´)
F(r,v)
F(r,v,a)
F(r,v,a: rperpendicular.to.v,a = 0)
F(r,v,a: v|rs|a)
F(r,v,t)
F(r - v*t,t)
FT
Fu_G
F_Weber
G
g
Gμv
H
HFLN
I
i
i´
inf
_inv
_inv(a,b)
_inv(a,β)
_inv(b,c)
_inv(β,c)
J
Jackson1999
J(r´)
J(r,t)
J(x´)
J(x)
∫[∇´•J(x´)/|x - x´|]
∇∫[∇•J(x)/|x - x|]
k
K1
k1
K2
k2
k3
k5
k6
L
l
∂(l)
lamda
Larmor_radiation_nonRel
∮[∂(l): B]
L_cap
∮[•(L_cap/2/π*dφ)′: Ei(r - v*t,t)]
∮[•(L_cap/2/π*∂(φ))′: Ei(r - v*t,t)]
∮[•∂(l)′: Ei(r - v*t,t)]
Len
∫[•∂(l): ET(r´,t´)]
∮[•∂(l),.over.∂Σ: ET]
L_pie
Lucas05_18Larmor_radiation_total_nonrelativistic
Lucas05_19
L(v)
L(vs)
M
m
mE
m_e
Mg
mg
mg1
mg2
mi
mi1
mi2
mm
Mu
N
n
_n
n´
N1
n1
N2
n2
n3
nh
of
P1
P2
P2(r)
P3
P3(r)
P_Lienard
P_Lienard_circular_accelerator_relativistic
P_rad
q
q´
q1
q2
Qenclosed
q_enclosed
R
r
∂r
∂(r)
r´
r1
r(1 - )
r(1 + )
r12
r(1 - ,2 + )
r(1 + ,2 - )
r(1 + ,2 + )
r2
r(2 - )
r(2 + )
r21
r(2 - ,1 - )
r(2 + ,1 - )
r(2 + ,1 + )
R_cap_edge
Re
∂[∂(r): Ei(r´,t)•θ´hat*r)
∂[∂(r): Ei(r´,t)•φ´hat*rs)
RFo
RFt
Rgh
Rh
rh
r´h
r_h
rh´
∫[∂(r): ∇•J(r,t)/|r - r´|]
∇∫[∂r: ∇•J(r,t)/|r - r´|]
RNpch
ro
rov
rperpendicular
∂[∂(r): r*A2]
∂[∂(r): r*A3]
∂[∂r: r*Ei(r´,t)•θ´]
Rs
rs
∂rs
r´s
Ruc
r´v
S
s
si
sin
sin(2*θ)
sin(2*θf)
sin(w1*t1 + P1)
sin(w2*t2 + P2)
sin(x + φ)
∂(sin(θ´))
sin(θ´)
sin(θ)
∫[∂(sin(θ´)),0.to.θ´: sin(θ´)]
∫[∂(sin(θ´)),0.to.θ´: sin(θ´)^3]
sin(θf)
sin(φ)
sin(ω*t)
sin(ω*t + φ)
sqrt
statC
Sum
sum
sum(F_real)
sum(k=0 to inf: choose(alpha,k)*x^k)
sum(k=0.to.inf: choose(alpha,k)*x^k)
sum(k = 0.to.inf: choose(alpha,k)*x^k)
sum(n=0 to ∞: choose( - m,n)*z^n)
sum(n = 0.to.∞: choose( - m,n)*z^n)
Sum(n = 0.to.inf: choose( - m,n)*z^n
sum(n=0 to inf: choose( - m,n)*z^n
t
∂t
∂(t)
∂[∂(t): 
∂[∂t:
t´
∫[∂(t),0.to.2*π: 1/2/π*∫[∂(φ),0.to.2*π: sin(x)cos(φ) - cos(x)*sin(φ)]]
∫[∂(t),0.to.2*π: 1/2/π*∫[∂(φ),0.to.2*π: sin(x + φ)]]
∫[∂(t),0.to.2*π: ∫[∂(φ),0.to.2*π: sin(x)cos(φ) - cos(x)*sin(φ)]]
∫[∂(t),0.to.2*π/ω: 1/2/π*∫[∂(φ),0.to.2*π: sin(ω*t + φ)]]
∫[∂(t),0.to.τ: 1/2/π*∫[∂(φ),0.to.2*π: sin(ω*t + φ)]]
t1
t2
∂[∂(t): ∫[∂(Area): B(r,t)•n]]
∂[∂(t): B]
∂[∂(t): Bi(r - v*t,t)]
∂[∂(t): Bi(r - v*t,t)•n′]
∂[∂(t): B(r´,t)]
∂[∂(t): B(r,t)]
∂[∂(t): |Ei(r - v*t,t)|]
∂[∂(t): Ei(r - v*t,t)]
∂[∂(t): Ei(r - v*t,t)*sin(θ´)]
∂[∂(t): Eis(r - v*t,t)]
∂[∂(t): ET]
∂[∂(t): K1]
∂[∂(t): K2]
∂[∂(t): q/c*vs*sin(θ´)/r´s^2*φ´hat]
∂[∂(t): |r - v*t|]
Tμv
∫[∂(t),τ1.to.τ2: 2/3/c^3*q^2*a^2]
∫[∂(t),τ1.to.τ2: 2/3/c^3*q^2*(∂[∂t: v])^2]
∫[∂(t),τ1.to.τ2: 2/3/c^3*q^2*γ^2*a^2]
∫[∂(t),τ1.to.τ2: 2/3/c^3*q^2*γ^2*∂[∂t: v)•∂[∂t: v]]
∫[∂(t),τ1.to.τ2: 2/3/c^3*q^2*γ^4*[a^2 - (βa)^2]
∫[∂(t),τ1.to.τ2: d2/dt2(v)•v]
∫[∂(t),τ1.to.τ2: F_rad•v]
∫[∂(t),τ1.to.τ2: Lucas05_18Larmor_radiation_total_nonrelativistic]
∫[∂(t),τ1.to.τ2: Lucas05_19:  = P_Lienard_circular_accelerator_relativistic]
∫[∂(t),τ1.to.τ2: P_rad]
U
U_b
U(r,v)
V
v
v´
v1
v2
vB
∇(v•Bi(r - v*t,t))
v*(∇•Bi(r - v*t,t))
v*(∇Bi(r - v*t,t))
v*B(rov,t)
vs
vt
v_X_r
w1
w2
Work_done_on_particle_by_EDF_to_emit_radiation_nonrelativistic
X
x
x´
y
Z
z
Z1
Z2
zz
α
β
β(∇a)
γ
ε0
θ
∂(θ´)
∂(θ)
θ´
∫[∂(θ),0.to.2*π: sin(θ)/(1 - β^2*sin(θ)^2)^(3/2)]
∫[∂(θ),0.to.2*π: sin(θ)/(1 - β^2*sin(θ)^2)^(3/2)]
∫[∂(θ),0.to.Of: 1/r/c*sin(θ)*∂[∂(t): Ei(r - v*t,t)]]
∫[∂(θ),0.to.Of: 1/r/c*sin(θ)*∂[∂(t): Ei(r - v*t,t)]
∫[∂(θ),0.to.Of: 1/r/c*sin(θ)*∂[∂(t): Ei(r - v*t,t)]]
∫[∂(θ),0.to.Of: 1/r/c*sin(θ)*∂[∂(t): K1]]
∫[∂(θ),0.to.Of: 1/r/c*sin(θ)*∂[∂(t): K2]]
∫[∂(θ´),0.to.Of: 1/rs/c*sin(θ´)*∂[∂(t): Eis(r - v*t,t)]]
∫[∂(θ),0.to.Of: 1/rs/c*sin(θ)*∂[∂(t): Eis(r - v*t,t)]]
∫[∂(θ),0.to.Of: 1/rs/c*∂[∂(t): Ei(r - v*t,t)]*sin(θ)]
∫[∂(θ),0.to.Of: sin(θ)^2]
∫[∂(θ´),0.to.θ´: 1/r/c*∂[∂(t): Ei(r - v*t,t)*sin(θ´)]]
∫[∂(θ´),0.to.θ´f: 1/rs/c*sin(θ´)*∂[∂(t): Ei(r - v*t,t)]]
∫[∂(θ´),0.to.θ´f: 1/rs/c*sin(θ´)*∂[∂(t): Eis(r - v*t,t)]]
∫[∂(θ´),0.to.θ´f: 1/rs/c*sin(θ)*∂[∂(t): Eis(r - v*t,t)]]
∫[∂(θ´),0.to.θ´f: 1/rs/c*sin(θ´)*∂[∂(t): K1]]
∫[∂(θ´),0.to.θ´f: 1/rs/c*sin(θ´)*∂[∂(t): K2]]
∫[∂(θ´),0.to.θ´f: 1/rs/c*∂[∂(t): Eis(r - v*t,t)]*sin(θ´)]
∫[∂(θ´),0.to.θ´f:  - 1/rs*∂[∂(θ´): Ei(r - v*t,t))*φ´]]
∫[∂(θ´),0.to.θ´f: 3*(vs/c)^2*rs*sin(θ´)*φ´*q*(rs*cos(θ´) - vs*t)/|r - v*t|^5]
∫[∂(θ´),0.to.θ´f: (r*cos(θ) - vs*t)/|r - v*t|^5*sin(θ´)]
∫[∂(θ´),0.to.θ´f: (rs*cos(θ´) - vs*t)/|r - v*t|^5*sin(θ´)]
∫[∂(θ´),0.to.θ´f: (rs*cos(θ´) - vs*t)*sin(θ´)/|r - v*t|^5]
∫[∂(θ´),0.to.θ´f: sin(θ´)*15/2*β^3*q/rs^4*sin(θ´)^2*cos(θ´)]
∫[∂(θ´),0.to.θ´f: sin(θ´)^3*cos(θ´)]
∫[∂(θ´),0.to.θ´f: sin(θ´)*( - 3)*cos(θ´)]
∫[∂(θ´),0.to.θ´f: sin(θ´)*( - 3)*β*q/rs^4*λ(v)*cos(θ´)]
∫[∂(θ´),0.to.θ´f: sin(θ´)*cos(θ´)]
∫[∂(θ´),0.to.θ´f: sin(θ´)*(rs*cos(θ´) - vs*t)]
∫[∂(θ´),0.to.θ´f: sin(θ´)/rs/c*∂[∂(t): Eis(r - v*t,t)]]
∫[∂(θ´),0.to.θ´f: sin(θ´)*sin(θ´)^2*cos(θ´)]
∫[∂(θ´),0.to.θ´f: vs/c*rs*sin(θ´)*φ´*1/rs/c*∂[∂(t): Eis(r - v*t,t)]]
∫[∂(θ´),0.to.θ´f: ∂[∂(θ´): Ei(r - v*t,t)]]
∫[∂(θ´),0.to.θ´: (r*cos(θ´) - v*t)/|r - v*t|^5*sin(θ´)]
∫[∂(θ),0.to.π: 1]
∫[∂(θ),0.to.π: 1 + 3/2*β^2*sin(θ)^2 + 15/8*β^4*sin(θ)^4 + 35/16*β^6*sin(θ)^6]
∫[∂(θ),0.to.π: 15/8*β^4*sin(θ)^4]
∫[∂(θ),0.to.π: (1 - β^2*sin(θ)^2)^( - 3/2)]
∫[∂(θ),0.to.π: (1 - λ(v))*E0(r)/(1 - β^2*sin(θ)^2)^(3/2)]
∫[∂(θ),0.to.π: 3/2*β^2*sin(θ)^2]
∫[∂(θ),0.to.π: 35/16*β^6*sin(θ)^6]
∫[∂(θ),0.to.π: E0*(1 - λ(v))*r*sin(O)/(1 - β^2*sin(θ)^2)^(3/2)]
∫[∂(θ),0.to.π: E0(r)*r*sin(θ)*(1 - λ(v))/(1 - β^2*sin(θ)^2)^(3/2)]
∫[∂(θ),0.to.π: ET*(1 - λ(v))*r*sin(O)/(1 - β^2*sin(θ)^2)^(3/2)]
∫[∂(θ),0.to.π: ET(r)nh]
∫[∂(θ),0.to.π: sin(θ)*((1 - 3*cos(θ)^2/2))]
∫[∂(θ),0.to.π: sin(θ)/(1 - β^2*sin(θ)^2)^(3/2)]
∫[∂(θ),0.to.π: sin(θ)]
∫[∂(θ),0.to.π: sin(θ)*( - 1/8 - 1/4*cos(θ)^2 + 3/8*cos(θ)^4)]
∫[∂(θ),0.to.π: sin(θ)/(1 - β^2*sin(θ)^2)^(3/2)]
∫[∂(θ),0.to.π: sin(θ)^2]
∫[∂(θ),0.to.π: sin(θ)*( - 3/8 - 9/4*cos(θ)^2 + 15/8*cos(θ)^4)]
∫[∂(θ),0.to.π: sin(θ)^4]
∫[∂(θ),0.to.π: sin(θ)^6]
∫[∂(θ),0.to.π: sin(θ)*k2]
∫[∂(θ),0.to.π: sin(θ)*k3]
∫[∂(θ),0.to.π: sin(θ)*k6]
∫[∂(θ), - 1.to.1: q^2/4/π/c^3*a^2*(1 - cos(θ´)^2)]
∂[∂(θ): (1 - β^2*sin(θ)^2)]
∂[∂(θ): (1 - β^2*sin(θ)^2)^( - 1/2)]
∂[∂(θ): A1]
∂[∂(θ): |Ei(r´,t)|]
∂[∂(θ): Ei(r´,t)]
∂[∂(θ): Ei(r´,t)•r´h]
∂[∂(θ): Ei(r´,t)*sin(θ)]
∂[∂(θ): Ei(r´,t)•φ´hat*sin(θ)]
∂[∂(θ´): Ei(r - v*t,t)]
∂[∂(θ): Ei(r - v*t,t)]
θf
θ´f
θh
θh´
θ´hat
θo
∂[∂(θ´): sin(θ´)]
∂[∂(θ): sin(θ)]
∂[∂(θ): sin(θ)]
∂[∂(θ´): sin(θ´)^4]
∂[∂(θ): sin(θ)*A3]
λ
λ(v)
μ0
ξ
π
ρ
∂Σ
τ
τ1
τ2
φ
∂φ
∂(φ)
∂φ´
φ´
∫[∂(φ),0.to.2*π: 1]
∫[∂(φ),0.to.2*π: E0*(1 - λ(v))*r^2*2/(1 - β^2)]
∫[∂(φ),0.to.2*π: E0*(1 - λ(v))*r^2*∫[∂(θ),0.to.π: sin(O)/(1 - β^2*sin(θ)^2)^(3/2)]]
∫[∂(φ),0.to.2*π: F(r,O,φ,A1,w1,t)]
∫[∂(φ),0.to.2*π: sin^4(ω*t + φ)]
∫[∂(φ),0.to.2*π: sin(x)cos(φ) - cos(x)*sin(φ)]
∫[∂(φ),0.to.2*π: sin(x + φ)]
∫[∂(φ),0.to.2*π: sin(ω*t + φ)]
∫[∂(φ),0.to.2*π: ∫[∂(θ),0.to.π: (1 - β^2*sin(θ)^2)^( - 3/2)]]
∫[∂(φ),0.to.2*π: ∫[∂(θ),0.to.π: (1 - λ(v))*E0(r)/(1 - β^2*sin(θ)^2)^(3/2)]]
∫[∂(φ),0.to.2*π: ∫[∂(θ),0.to.π: E0(r)*r*sin(θ)*(1 - λ(v))/(1 - β^2*sin(θ)^2)^(3/2)]]
∫[∂(φ),0.to.2*π: ∫[∂(θ),0.to.π: ET(r)nh]]
∫[∂(φ),0.to.2*π: φ]
∂[∂(φ): A1]
∂[∂(φ): A2]
φ_cap
∂[∂(φ): Ei(r´,t)•r´h]
∂[∂(φ): Ei(r´,t)•θ´hat]
∮[•∂(φ)′: Ei(r - v*t,t)]
∮[•∂(φ)′: Ei(r - v*t,t)]
φh
φ´h
φ´hat
φ_pie
φ(r)
∮[*∂(φ)′: ∂[∂(t): Bi(r - v*t,t)]•n′]
ψ
ψ(r)
ω
Ω_cap
Ω_circle
Ω_full_sphere