Mixed Boundary Value Problems in Potential Theory |
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Page 29
... Hankel's inversion theorem states that f ( x ) = H , { g ( y , v ) ; x } ( 2.1.24 ) so that the inverse operator H1 = H ,. We call H , { ƒ ( x ) ; y } the Hankel Trans- form of order v of f ( x ) so that the Hankel transform is self ...
... Hankel's inversion theorem states that f ( x ) = H , { g ( y , v ) ; x } ( 2.1.24 ) so that the inverse operator H1 = H ,. We call H , { ƒ ( x ) ; y } the Hankel Trans- form of order v of f ( x ) so that the Hankel transform is self ...
Page 52
... Hankel Transforms and the Erdélyi- Kober Operators Between the Erdélyi - Kober operators of fractional integration on the one hand and the modified operator of the Hankel transform on the other we have a set of interesting relations ...
... Hankel Transforms and the Erdélyi- Kober Operators Between the Erdélyi - Kober operators of fractional integration on the one hand and the modified operator of the Hankel transform on the other we have a set of interesting relations ...
Page 279
... transforms , 47 External cracks , 16 Finite Legendre transforms , 69 Fourier - Bessel expansion , 37 , 134 , 137 , 139 ... Hankel kernel , 84-93 , 106-118 Hankel transform , 29 Heins - McCamy solution , 79 Hilbert - Schmidt theorem , 203 ...
... transforms , 47 External cracks , 16 Finite Legendre transforms , 69 Fourier - Bessel expansion , 37 , 134 , 137 , 139 ... Hankel kernel , 84-93 , 106-118 Hankel transform , 29 Heins - McCamy solution , 79 Hilbert - Schmidt theorem , 203 ...
Contents
THE OCCURRENCE OF MIXED BOUNDARY VALUE PROBLEMS IN POTENTIAL | 1 |
MATHEMATICAL PRELIMINARIES | 26 |
DUAL SERIES EQUATIONS | 37 |
6 other sections not shown
Common terms and phrases
axisymmetric Bessel function boundary conditions boundary value problems coefficients consider continuously differentiable cos(n cosh cosu cosx defined by equation denotes derived determination dual integral equations dual relations dual series equations dual series relations electrified disk electrostatic equa equivalent Erdélyi formula fractional integral Fredholm equation Fredholm integral equation free term function f(x g₁(x given by equation h₁(t h₁(x half-space Hankel Hankel transform harmonic function I₁ interchange the order it)² Jacobi polynomial kernel L₁(x Laplace's equation Math method mixed boundary value obtain the relation operator pair of dual pair of equations plane potential function potential theory prescribed R₁ reduces result S₁ satisfies side of equation Similarly sin(n Sneddon solution solve spherical cap substitute from equation Substituting this expression tion u)du V₁ V₂ write xel₁ xel2 дф