1.
(a+x)n=
∑
n k=0
n k
xkan−k (A.88)
2.
φx(jω) =
∫∞ 0
fx(x)ejωxdx (A.89)
3.
fx(x) = 1 2π
∫∞
−∞
φx(jω)e−jωxdω (A.90)
4.
∫∞ 0
xn−1e−βxdx=Γ(m)β−n,n>0 (A.91) 5.
∫∞
−∞
(β−ix)−ve−ipxdx=2πpv−1e−βp
Γ(v) ,p>0 (A.92)
6.
y=ax,fy(y) = 1 afx
(y a
)
(A.93) 7.
Γ(z) =
∫∞ 0
e−ttz−1dt (A.94)
8.
∫u
0
xβ−1e−µxdx=µ−βν(β,µu),β>0 (A.95) 9.
ν(α,x) =
∫x
0
e−ttα−1dt,α>1 (A.96) 10.
ν(1+n,x) =n!
[ 1−ex
∑
n m=0xm m!
]
,n= [0,1, . . .] (A.97) 11.
Γ(x) = (x−1)! (A.98)
12.
Q(√
2gγ) = 1 π
π2
∫
0
exp (
− gγ sin2θ
)
dθ (A.99)
13.
Iv(z) = (z
2 )v ∞
k=0
∑
(z2/2)k
k!Γ(v+k+1) (A.100)
14.
∫∞ 0
xv−1e−βx2−γxdx= (2β)−v/2Γ(v)exp (γ2
8β )
D−v (√γ
2β )
[Re{β}>0,Re{v}>0]
(A.101) 15.
Dp(z) =22pe−z
2 4
√π Γ(1−
p 2
)Φ [
−p 2,1
2,z2 2
]
−
√2πz Γ(
−2p)Φ
[1−p 2 ,3
2,z2 2
]}
(A.102)
16.
y=xn,fy(y) = 1
ny(1−nn)fx
( y1n
)
y>0 (A.103)
17.
y=cosx,fy(y) = 2
√1−y2fx(x) (A.104)
18.
z=xy,fz(z) =
∫∞ 0
1
xfx(x)fy(z/x)dx (A.105) 19.
Γ(nx) = (2π)1−2nnnx−12
n−1
∏
k=0
Γ (
x+k n
)
(A.106)
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