Page 310 - Handbook Of Integral Equations

b cot(βx)

47. y(x) – λ y(t) dt = f(x).
a cot(βt)
1
This is a special case of equation 4.9.1 with g(x) = cot(βx) and h(t)= .
cot(βt)
b cot(βt)
48. y(x) – λ y(t) dt = f(x).
a cot(βx)
1
This is a special case of equation 4.9.1 with g(x)= and h(t) = cot(βt).
cot(βx)
b
k
m
49. y(x) – λ cot (βx) cot (µt)y(t) dt = f(x).
a
m
k
This is a special case of equation 4.9.1 with g(x) = cot (βx) and h(t) = cot (µt).
b

m
k
50. y(x) – λ t cot (βx)y(t) dt = f(x).
a
m
k
This is a special case of equation 4.9.1 with g(x) = cot (βx) and h(t)= t .
b
k
m
51. y(x) – λ x cot (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) = cot (βt).

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

53. y(x) – λ [A + B(x – t) cot(βx)]y(t) dt = f(x).
a
This is a special case of equation 4.9.10 with h(x) = cot(βx).
4.5-5. Kernels Containing Combinations of Trigonometric Functions
b

m
k
54. y(x) – λ cos (βx) sin (µt)y(t) dt = f(x).
a
m
k
This is a special case of equation 4.9.1 with g(x) = cos (βx) and h(t) = sin (µt).
b
55. y(x) – λ [A sin(αx) cos(βt)+ B sin(γx) cos(δt)]y(t) dt = f(x).
a
This is a special case of equation 4.9.18 with g 1 (x)=sin(αx), h 1 (t)=A cos(βt), g 2 (x)=sin(γx),
and h 2 (t)= B cos(δt).
b
m
k
56. y(x) – λ tan (γx) cot (µt)y(t) dt = f(x).
a
k
m
This is a special case of equation 4.9.1 with g(x) = tan (γx) and h(t) = cot (µt).
b

57. y(x) – λ [A tan(αx) cot(βt)+ B tan(γx) cot(δt)]y(t) dt = f(x).
a
This is a special case of equation 4.9.18 with g 1 (x)=tan(αx), h 1 (t)=A cot(βt), g 2 (x)=tan(γx),
and h 2 (t)= B cot(δt).

© 1998 by CRC Press LLC

© 1998 by CRC Press LLC
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