Page 320 - Handbook Of Integral Equations

b

m
k
47. y(x) – λ cos (βt)ln (µx)y(t) dt = f(x).
a
m k
This is a special case of equation 4.9.1 with g(x)=ln (µx) and h(t) = cos (βt).
b
k
m
48. y(x) – λ sin (βx)ln (µt)y(t) dt = f(x).
a
k
m
This is a special case of equation 4.9.1 with g(x) = sin (βx) and h(t)=ln (µt).
b
m
k
49. y(x) – λ sin (βt)ln (µx)y(t) dt = f(x).
a
m
k
This is a special case of equation 4.9.1 with g(x)=ln (µx) and h(t) = sin (βt).
b
k
m
50. y(x) – λ tan (βx)ln (µt)y(t) dt = f(x).
a
m
k
This is a special case of equation 4.9.1 with g(x) = tan (βx) and h(t)=ln (µt).

b
k
m
51. y(x) – λ tan (βt)ln (µx)y(t) dt = f(x).
a
m k
This is a special case of equation 4.9.1 with g(x)=ln (µx) and h(t) = tan (βt).
b

m
k
52. y(x) – λ cot (βx)ln (µt)y(t) dt = f(x).
a
m
k
This is a special case of equation 4.9.1 with g(x) = cot (βx) and h(t)=ln (µt).
b
k
m
53. y(x) – λ cot (βt)ln (µx)y(t) dt = f(x).
a
k
m
This is a special case of equation 4.9.1 with g(x)=ln (µx) and h(t) = cot (βt).
4.8. Equations Whose Kernels Contain Special
Functions
4.8-1. Kernels Containing Bessel Functions

b
1. y(x) – λ J ν (βx)y(t) dt = f(x).
a
This is a special case of equation 4.9.1 with g(x)= J ν (βx) and h(t)=1.
b
2. y(x) – λ J ν (βt)y(t) dt = f(x).
a
This is a special case of equation 4.9.1 with g(x) = 1 and h(t)= J ν (βt).

∞
1
3. y(x)+ λ tJ ν (xt)y(t) dt = f(x), ν > – .
2
0
Solution:
f(x) λ ∞
y(x)= – tJ ν (xt)f(t) dt, λ ≠ ±1.
1 – λ 2 1 – λ 2
0
© 1998 by CRC Press LLC

© 1998 by CRC Press LLC
Page 299