| Preface |
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vii | |
| Introduction |
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1 | (4) |
Part
1. Foundation of the theory of Bessel functions |
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5 | (126) |
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The Bessel equation. Properties of Bessel functions |
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7 | (58) |
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The Bessel differential equation. Application of power series. Cylindrical functions of the first kind |
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7 | (3) |
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Cylindrical functions of the second kind (Neumann functions) |
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10 | (1) |
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Cylindrical functions of the third kind (Hankel functions) |
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11 | (1) |
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Cylindrical functions of a pure imaginary argument |
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11 | (1) |
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Cylindrical functions of a complex argument |
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12 | (2) |
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Formulae of differentiation, recurrence relations |
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14 | (2) |
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Cylindrical functions with a half-integer index |
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16 | (1) |
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Some notation for functions of half-integer and fractional index. Airy integral |
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17 | (2) |
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19 | (3) |
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Bessel integral and Jacobi expansion |
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22 | (4) |
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26 | (5) |
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31 | (1) |
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Differential equations reducible to the Bessel equation |
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31 | (6) |
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37 | (3) |
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Some indefinite integrals |
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40 | (3) |
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Functions contiguous to Bessel functions. Particular solutions of the inhomogeneous Bessel equation |
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43 | (7) |
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On integration of the inhomogeneous Bessel equation. Cauchy functions |
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50 | (6) |
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Products of Bessel functions |
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56 | (3) |
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Integral representations of Bessel functions |
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59 | (6) |
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Definite and improper integrals. Series in Bessel functions |
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65 | (66) |
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65 | (4) |
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69 | (18) |
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87 | (6) |
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Roots of the Bessel functions |
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93 | (3) |
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Series of Fourier-Bessel and Dini |
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96 | (8) |
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104 | (9) |
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113 | (1) |
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Lommel functions of two variables |
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114 | (6) |
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On partial cylindrical functions |
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120 | (5) |
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Asymptotic expansion of Bessel functions |
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125 | (3) |
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On Bessel functions with a large index |
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128 | (3) |
Part
2. Applications of Bessel functions |
|
131 | (134) |
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Problems of the theory of plates and shells |
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133 | (82) |
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Oscillations and stability of a circular plate |
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133 | (22) |
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Equilibrium of a circular plate lying on an elastic foundation. Axially symmetrical deformation |
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155 | (7) |
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Equilibrium of a circular plate lying on an elastic foundation. Nonaxially symmetrical deformation |
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162 | (8) |
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Calculation of a circular conic shell under the action of axially symmetrical loadings and non-uniform heating |
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170 | (14) |
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The method of compensating loadings in problems on membranes and plates |
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184 | (24) |
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The problem on equilibrium of an unbounded plate which lies on a uniform elastic foundation whose model has a circular symmetry |
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208 | (7) |
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Problems of the theory of oscillations, hydrodynamics and heat transfer |
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215 | (50) |
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On the oscillations of a thread |
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215 | (4) |
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Stability and transverse-longitudinal bending of a rectilinear rod; stability of the plane form of the bending of a strip |
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219 | (22) |
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Plane heat waves in a half-space and a layer; heat waves in a rod |
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241 | (6) |
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A die which lies on an elastic half-space whose modulus of elasticity is a power function of the depth |
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247 | (3) |
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Application of integral equations to the solution of some problems on membranes and plates |
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250 | (6) |
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On wave propagation in electric power lines |
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256 | (1) |
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The action of an impulse on cylindrical and prismatic tanks filled with a fluid |
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257 | (8) |
| Appendix A. Brief information on gamma functions |
|
265 | (2) |
| Bibliographical notes |
|
267 | (4) |
| Bibliography |
|
271 | (4) |
| Index |
|
275 | |
