Page 314 - Handbook Of Integral Equations

4.6-4. Kernels Containing Arccotangent

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

b

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

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

b arccot(βx)

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

b arccot(βt)

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

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

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

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

© 1998 by CRC Press LLC

© 1998 by CRC Press LLC
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