Lectures on Transform MethodsNorth Carolina State University, Applied Mathematics Research Group, 1967 - Elastic solids - 104 pages Contents: The Stress Intensity Factor for a Griffith Crack in an Elastic Body in which Body Forces are acting; The Stress Intensity Factor for a Penny-Shaped Crack in an Elastic Body under the Action of Symmetric Body Forces -- The Effect of Two Point Forces Symmetrically Placed; Inversion Formulae for Integral Transform Pairs of General Kinds -- Properties of the Mellin Transform, Y - Transforms, Integral equations of Abel type, Transforms whose kernels are Chebyshev polynomials, Legendre polynomials, Gegenbauer polynomials, Associated Legendre functions, and Hypergeometric functions; The Inversion of Hankel Transforms of Order Zero and Unity; and Lectures on Kontorovich-Lebedev Transforms and Some of their Applications -- Solutions of Bessel's Modified Equation, The Macdonald Function, Table of Kontorovich-Lebedev Transforms, Parseval Relation for Kontorovich-Lebedev Transforms, Functions which are Harmonic in an Infinite Wedge, in a Semi-Infinite Wedge, in a Wedge of Finite Thickness, and Applications in the Theory of Elasticity. |
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Page 28
... function of the second kind . In recent years there have appeared inversion formula for several integral transforms ... hypergeometric function . The case in which K ( x ) = ( 1 − x2 ) −1/2 г_ ( x ̄1 ) , T ̧ being the Chebyshev - n Τ n ...
... function of the second kind . In recent years there have appeared inversion formula for several integral transforms ... hypergeometric function . The case in which K ( x ) = ( 1 − x2 ) −1/2 г_ ( x ̄1 ) , T ̧ being the Chebyshev - n Τ n ...
Page 55
... hypergeometric series we find that [ 1/2 1 + x 1 T_ ( x ) = F + n , n 2 글 - 1 n ; 끓 그늘 지 - X 2 [ from which it ... function with argument 1/2 - n ; s + 글 을 on the right hand side of this last equation can be summed by the use of ...
... hypergeometric series we find that [ 1/2 1 + x 1 T_ ( x ) = F + n , n 2 글 - 1 n ; 끓 그늘 지 - X 2 [ from which it ... function with argument 1/2 - n ; s + 글 을 on the right hand side of this last equation can be summed by the use of ...
Page 68
... hypergeometric function transform " J. Soc . Indust . Appl . Math . 12 , 601 1960 " A new class of integral transforms " Proc . Amer . Math . Soc . 11 , 290 L. J. Slater , 1966 " Generalized Hypergeometric Functions " ( Cambridge ...
... hypergeometric function transform " J. Soc . Indust . Appl . Math . 12 , 601 1960 " A new class of integral transforms " Proc . Amer . Math . Soc . 11 , 290 L. J. Slater , 1966 " Generalized Hypergeometric Functions " ( Cambridge ...
Contents
References | 7 |
Transforms whose kernels are hypergeometric functions | 12 |
The Stress Intensity Factor for a PennyShaped Crack in an Elastic | 14 |
4 other sections not shown
Common terms and phrases
apply the operator Bessel function body force Z(p,z boundary conditions calculate components cos(vt)dt cosh deduce immediately defined by equation denotes derived distribution of body equation 3.1 equation 5.5 equations 2.8 equations of elastic equivalent Erdélyi F₂ Fourier cosine transform Fourier inversion theorem Fourier sine transform Fourier Transforms function p(p given Griffith crack Hankel transform harmonic hence hypergeometric function hypergeometric series I. N. Sneddon integral equation integral transform inversion formula inversion theorem Kontorovich-Lebedev transform magnitude F act Math Mellin transform obtain the equation odd function penny-shaped crack point forces Poisson's ratio polynomial Proc relation result sinh sinh(2ar solution of Problem stress intensity factor substitute from equation transform of order πο ᎩᎩ ᏃᏃ 글이 미글 미를