Page 302 - Handbook Of Integral Equations

b
m
k
6. y(x) – λ ln (γx)ln (µt)y(t) dt = f(x).
a
m
k
This is a special case of equation 4.9.1 with g(x)=ln (γx) and h(t)=ln (µt).
4.4-2. Kernels Containing Power-Law and Logarithmic Functions

b
k
m
7. y(x) – λ t ln (γx)y(t) dt = f(x).
a
k
m
This is a special case of equation 4.9.1 with g(x)=ln (γx) and h(t)= t .
b
k
m
8. y(x) – λ x ln (γt)y(t) dt = f(x).
a
m
k
This is a special case of equation 4.9.1 with g(x)= x and h(t)=ln (γt).

b
9. y(x) – λ [A + B(x – t) ln(γt)]y(t) dt = f(x).
a
This is a special case of equation 4.9.8 with h(t) = ln(γt).
b

10. y(x) – λ [A + B(x – t) ln(γx)]y(t) dt = f(x).
a
This is a special case of equation 4.9.10 with h(x) = ln(γx).

b
11. y(x) – λ [A +(Bx + Ct) ln(γt)]y(t) dt = f(x).
a
This is a special case of equation 4.9.9 with h(t) = ln(γt).

b
12. y(x) – λ [A +(Bx + Ct) ln(γx)]y(t) dt = f(x).
a
This is a special case of equation 4.9.11 with h(x) = ln(γx).
b
n
m
k
l
13. y(x) – λ [At ln (βx)+ Bx ln (γt)]y(t) dt = f(x).
a
k
m
n
This is a special case of equation 4.9.18 with g 1 (x)=ln (βx), h 1 (t)= At , g 2 (x)= x , and
l
h 2 (t)= B ln (γt).
4.5. Equations Whose Kernels Contain Trigonometric
Functions
4.5-1. Kernels Containing Cosine

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

© 1998 by CRC Press LLC

© 1998 by CRC Press LLC
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