Page 60 - Handbook Of Integral Equations

x

λ µ β γ
108. Ax sinh t + Bt cosh x y(t) dt = f(x).
a
γ
µ
λ
This is a special case of equation 1.9.15 with g 1 (x)= Ax , h 1 (t) = sinh t, g 2 (x)= B cosh x,
β
and h 2 (t)= t .
x

109. A tanh(λx)+ B coth(µt)+ C y(t) dt = f(x).
a
This is a special case of equation 1.9.6 with g(x)= A tanh(λx) and h(t)= B coth(µt)+ C.
x

2 2
110. A tanh (λx)+ B coth (µt) y(t) dt = f(x).
a
2
2
This is a special case of equation 1.9.6 with g(x) = tanh (λx) and h(t)= B coth (µt).
x

111. tanh(λx) coth(µt) + tanh(βx) coth(γt) y(t) dt = f(x).
a
This is a special case of equation 1.9.15 with g 1 (x) = tanh(λx), h 1 (t) = coth(µt), g 2 (x)=
tanh(βx), and h 2 (t) = coth(γt).
x

112. coth(λx) tanh(µt) + coth(βx) tanh(γt) y(t) dt = f(x).
a
This is a special case of equation 1.9.15 with g 1 (x) = coth(λx), h 1 (t) = tanh(µt), g 2 (x)=
coth(βx), and h 2 (t) = tanh(γt).

x

113. tanh(λx) tanh(µt) + coth(βx) coth(γt) y(t) dt = f(x).
a
This is a special case of equation 1.9.15 with g 1 (x) = tanh(λx), h 1 (t) = tanh(µt), g 2 (x)=
coth(βx), and h 2 (t) = coth(γt).
x

β γ
114. A tanh (λx)+ B coth (µt) y(t) dt = f(x).
a
β γ
This is a special case of equation 1.9.6 with g(x)= A tanh (λx) and h(t)= B coth (µt).
x

β γ
115. A coth (λx)+ B tanh (µt) y(t) dt = f(x).
a
β
γ
This is a special case of equation 1.9.6 with g(x)= A coth (λx) and h(t)= B tanh (µt).
x
λ µ β γ
116. Ax tanh t + Bt coth x y(t) dt = f(x).
a
µ
γ
λ
This is a special case of equation 1.9.15 with g 1 (x)= Ax , h 1 (t) = tanh t, g 2 (x)= B coth x,
β
and h 2 (t)= t .
x

λ µ β γ
117. Ax coth t + Bt tanh x y(t) dt = f(x).
a
γ
µ
λ
This is a special case of equation 1.9.15 with g 1 (x)= Ax , h 1 (t) = coth t, g 2 (x)= B tanh x,
β
and h 2 (t)= t .
© 1998 by CRC Press LLC

© 1998 by CRC Press LLC
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