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b
8. y(x) – λ [A + B(x – t) arccos(βx)]y(t) dt = f(x).
a
This is a special case of equation 4.9.10 with h(x) = arccos(βx).
b
9. y(x) – λ [A + B(x – t) arccos(βt)]y(t) dt = f(x).
a
This is a special case of equation 4.9.8 with h(t) = arccos(βt).

4.6-2. Kernels Containing Arcsine

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

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

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

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

b
k
m
14. y(x) – λ arcsin (βx) arcsin (µt)y(t) dt = f(x).
a
k
m
This is a special case of equation 4.9.1 with g(x) = arcsin (βx) and h(t) = arcsin (µt).
b
k
m
15. y(x) – λ t arcsin (βx)y(t) dt = f(x).
a
m
k
This is a special case of equation 4.9.1 with g(x) = arcsin (βx) and h(t)= t .
b
k
m
16. y(x) – λ x arcsin (βt)y(t) dt = f(x).
a
k
m
This is a special case of equation 4.9.1 with g(x)= x and h(t) = arcsin (βt).
b
17. y(x) – λ [A + B(x – t) arcsin(βt)]y(t) dt = f(x).
a
This is a special case of equation 4.9.8 with h(t) = arcsin(βt).

b
18. y(x) – λ [A + B(x – t) arcsin(βx)]y(t) dt = f(x).
a
This is a special case of equation 4.9.10 with h(x) = arcsin(βx).

© 1998 by CRC Press LLC

© 1998 by CRC Press LLC
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