Page 300 - Handbook Of Integral Equations

4.3-4. Kernels Containing Hyperbolic Cotangent

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

b

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

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

b coth(βx)

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

b coth(βt)

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

m
k
45. y(x) – λ coth (βx) coth (µt)y(t) dt = f(x).
a
k
m
This is a special case of equation 4.9.1 with g(x) = coth (βx) and h(t) = coth (µt).
b
m
k
46. y(x) – λ t coth (βx)y(t) dt = f(x).
a
k
m
This is a special case of equation 4.9.1 with g(x) = coth (βx) and h(t)= t .
b
k
m
47. y(x) – λ x coth (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) = coth (βt).
b
48. y(x) – λ [A + B(x – t) coth(βt)]y(t) dt = f(x).
a
This is a special case of equation 4.9.8 with h(t) = coth(βt).

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

© 1998 by CRC Press LLC

© 1998 by CRC Press LLC
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