Page 313 - Handbook Of Integral Equations

4.6-3. Kernels Containing Arctangent

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

b

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

b
21. y(x) – λ [A arctan(βx)+ B arctan(βt)]y(t) dt = f(x).
a
This is a special case of equation 4.9.4 with g(x) = arctan(βx).

b arctan(βx)

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

b arctan(βt)

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

m
k
24. y(x) – λ arctan (βx) arctan (µt)y(t) dt = f(x).
a
k
m
This is a special case of equation 4.9.1 with g(x) = arctan (βx) and h(t) = arctan (µt).
b

m
k
25. y(x) – λ t arctan (βx)y(t) dt = f(x).
a
k
m
This is a special case of equation 4.9.1 with g(x) = arctan (βx) and h(t)= t .
b
m
k
26. y(x) – λ x arctan (βt)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) = arctan (βt).
b
27. y(x) – λ [A + B(x – t) arctan(βt)]y(t) dt = f(x).
a
This is a special case of equation 4.9.8 with h(t) = arctan(βt).

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

© 1998 by CRC Press LLC

© 1998 by CRC Press LLC
Page 292