Page 299 - Handbook Of Integral Equations

4.3-3. Kernels Containing Hyperbolic Tangent

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

b

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

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

b tanh(βx)

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

b tanh(βt)

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

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

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

© 1998 by CRC Press LLC

© 1998 by CRC Press LLC
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