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| Авторизация |
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| Поиск по указателям |
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| Rainville E. D. — Intermediate Course in Differential Equations |
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| Предметный указатель |
 183
 183
 183
 183
Abel 48 133
Abel's formula 48
Adjoint 9
Adjoint, invariant of 10
Analytic continuation 62
Analytic function 26 54
applications 192—209
Bateman 177
Bernoulli numbers 61
Bernoulli, Jacob 61
bessel 96
Bessel functions of index zero, application 200
Bessel functions of index zero, orthogonality of 201
Bessel functions of the second kind, Neumann's 181
Bessel — Clifford equation 183
Bessel's equation of index n 180
Bessel's equation of index n, applications of 197 198
Bessel's equation of index n, obtained by confluence from Fuchsian equation 167
Bessel's equation of index two 105
Bessel's modified equation of index n 182
Bessel's modified equation of index zero 96
Bilinear transformation 18 65
Boundary-value problem 199 206
Cauchy 54
Cauchy product of series 72
Cauchy — Riemann equations 54
Change of both variables 19
Change of dependent variable 2
Change of independent variable 12
Circular plate, deformation of 193
Confluence of Fuchsian equation into Bessel's equation 167
Confluence of Fuchsian equation with three singular points 165
Confluence of hypergeometric equation into Bessel's equation of index zero 163
Confluence of singularities 163
Confluent hypergeometric equation, Pochhammer — Barnes 190
Confluent hypergeometric equation, Whittaker's 169 171
Conformal mapping 63
Contiguous functions 159
Crelle 133
Cross-ratio group 46 153
Cross-ratio of solutions of Riccati equation 45
Differential operator, factorization of 21 30 43
Differential operator, proper divisor 44
Equivalence of two second-order equations 7
Equivalence of two second-order equations, under change of both variables 19
Essential singularity of a function 56
Euler 96 145
Euler's constant 100
Existence theorem on solution near a regular singular point 90
Existence theorem on solution near an ordinary point 83
Exponents of an equation at a regular singular point 87
Fuchs 130 132 133
Fuchsian equation 130
Fuchsian equation of order n 133
Fuchsian equation with (m+1) singularities 132 134
Fuchsian equation with 3 singularities 135
Fuchsian equation with 4 singularities 137
Fuchsian invariant 135
Gauss 136 145 159
Generating function for Hermite polynomials 187
Generating function for Laguerre polynomials 190 209
Heat equation 199 209
Hermite polynomials 187
Hermite polynomials, generating function for 187
Hermite polynomials, orthogonality of 189
Holomorphic 54
Hutchinson 53 56
Hypergeometric equation 142 144
Hypergeometric equation, general solution of 148
Hypergeometric equation, Kummer's 24 solutions of 157
Hypergeometric function, derivative of 162
Hypergeometric function, special cases of 160
Hypergeometric series 145
In variance of Schwarzian Derivative 17
Indicial equation 87
Integrating factor 9
Invariant in normal form of second-order equation 6
Invariant, Fuchsian 135
Invariants under change of independent variable 29 30
Involution 10
Isolated essential singularity 56
Kelvin 183
Kelvin's ber and bei functions 183
| Kelvin's ber and bei functions, application of 193
Kelvin's ber and bei functions, equation satisfied by 185
Kummer 158
Kummer's 24 solutions of the hypergeometric equation 157
Kummer's first formula 175
Laguerre polynomials 189 191 209
Laguerre polynomials, generalized 189
Laguerre polynomials, generating function for 190 209
Laguerre polynomials, orthogonality of 190
Laplace's equation 206 209
Laurent series 59
legendre 160
Legendre polynomials 160 185
Legendre polynomials, orthogonality of 186
Legendre's equation 161 185 207
Legendre's equation, associated 186
Linear equation of second order with only one singularity 135
Linear fractional transformation 18 65
Liouville 57
Liouville's theorem 57
Mascheroni's constant 100
Modified Bessel equation of index n 182
Modified Bessel equation of index zero 96
Multiplication of series 72
Natural boundary 63
Neumann Bessel function of the second kind 181
Neumann sphere 56
Normal form of second-order equation 5
Operators, factorization of 21 30 43
Operators, factorization of, proper divisor of 44
Ordinary points of second-order equation 79
Ordinary points of second-order equation, solution valid near 80
Ordinary points of second-order equation, solution valid near, existence theorem 83
Orthogonality of Bessel functions 201
Orthogonality of Hermite polynomials 189
Orthogonality of Laguerre polynomials 190
Orthogonality of Legendre polynomials 186
Papperitz 139
Penstock design, a detail in 192
Pochhammer — Barnes confluent hypergeometric function 190
Pochhammer — Barnes confluent hypergeometric function, application of 195
Pole 56
Polynomial solutions of partial differential equations 208
Polynomial solutions of Riccati equations 36
Power series 58
Power series, inequality on coefficients in 62
Power series, multiplication of 72
Power series, radius of convergence of 58
Regular singular point 85
Regular singular point, solution valid near 86
Regular singular point, solution valid near, existence theorem 90
Riccati 31
Riccati equation 31
Riccati equation with (n+1) polynomial solutions 51
Riccati equation with 5 polynomial solutions 42
Riccati equation with 6 polynomial solutions 52
Riccati equation with given general solution 51
Riccati equation, application of 197
Riccati equation, form of general solution 34
Riccati equation, polynomial solutions of 36
Riccati equation, relation to second-order equation 32
Riccati equation, solution, when 3 particular solutions are known 47
Riccati equation, solution, when a particular solution is known 32
Riccati problem 31
Riemann 54 159
Riemann P-function 140
Riemann — Papperitz equation 137
Schwarzian derivative 16
Self-adjoint 11
Single-valued function 53
Singularities of functions 55
Singularities of second-order equation 83
Singularities of second-order equation, regular 85
Singularities of second-order equation, regular, solution valid near 86
Singularities of solutions of a differential equation 84
Temperatures in a cylinder 198
Transformation of both variables 19
Transformation of dependent variable 2
Transformation of independent variable 12
Transformation, bilinear or linear fractional 18 65
Whitehead 184
Whittaker 171
Whittaker's confluent hypergeometric function 176
Whittaker's equation 169 171
Whittaker's equation, solutions of 174
Wronski 47
wronskian 47
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