Dual Series Relations: Lectures Given in the Department of Mathematics, North Carolina State College, Raleigh in March 1963 |
Common terms and phrases
associated Legendre associated Legendre polynomials assume axis Bessel function boundary conditions boundary value problems coefficients constants cos(n cose cylinder defined by equation determine dual integral equations Dual Relations involving dual series equations dual series relations Erdelyi-Kober Operators Fourier-Bessel Fourier-Bessel Series Fredholm equation Fredholm integral equation function g(t given by equations integration and summation interchange the order J₁ J₂ Jacobi polynomial kernel Laplace's equation Legendre polynomial obtain the relation P(cos P₁ P₁₂ pair of dual pair of equations positive zeros prescribed right-hand side satisfy the dual series relations involving side of equation sin(n sin(x sinh Sneddon solution of equations spherical cap Srivastav 1963 Substituting this expression summation and integration t)at u)du λ λ π π др