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Lewin L. — Polylogarithms and Associated Functions
Lewin L. — Polylogarithms and Associated Functions

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Название: Polylogarithms and Associated Functions

Автор: Lewin L.

Язык: en

Рубрика: Математика/Анализ/Специальные функции/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1981

Количество страниц: 363

Добавлена в каталог: 12.04.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Abel, N. H.      8 18 28 31 93 135 174 177 238 240 262 269 356
Adams, J. C.      312
Andrews, C.      145
Appell      236
Ashour, A.      28 313
Bernoulli, J.      189 356
Bernoulli, numbers      193
Bernoulli, polynomials      200 236
Bertrand      18 28
Blissard, J.      23
Boehm. J.      115
Borsellino, A.      32
Bowman. F.      219 227
Clausen      32 33 35 69 73 102 158 191 246 312
Clausen, function      101
Clausen, function, addition equation      110 115
Clausen, function, expansion      105 106
Clausen, function, factorization formula      104
Clausen, function, functional equation      108
Clausen, function, geometric relations      115
Clausen, function, particular values      103 106 107
Clausen, function, periodic properties      102
Clausen, function, relation to $\rm {ImLi}_{2}$      110 121
Clausen, function, relation to $\rm {Ti}_{2}$      106 107
Corrington, M. S.      28 313
Coxeter, H. S. M.      115 118
de Doelder, P. J.      23 267
definitions      27
Dilogarithm $\rm {Li}_{2}(z),$ branch cut      2
Dilogarithm $\rm {Li}_{2}(z),$ factorization formula      6
Dilogarithm $\rm {Li}_{2}(z),$ functional equations, many variables      16 18
Dilogarithm $\rm {Li}_{2}(z),$ functional equations, single variable      4 5 10 11
Dilogarithm $\rm {Li}_{2}(z),$ functional equations, two variables      8 9 10 13
Dilogarithm $\rm {Li}_{2}(z),$ integral equations      23—27
Dilogarithm $\rm {Li}_{2}(z),$ inversion relation      4
Dilogarithm $\rm {Li}_{2}(z),$ numerical relations      6 117 144 145
Dilogarithm $\rm {Li}_{2}(z),$ series expansions      21
Dilogarithm of complex argument $\rm {Li}_{2}(r,\theta),$ addition formula for the angle      141 147
Dilogarithm of complex argument $\rm {Li}_{2}(r,\theta),$ factorization formula      123
Dilogarithm of complex argument $\rm {Li}_{2}(r,\theta),$ functional equations, derived      134
Dilogarithm of complex argument $\rm {Li}_{2}(r,\theta),$ functional equations, inversion relation      126
Dilogarithm of complex argument $\rm {Li}_{2}(r,\theta),$ functional equations, single variable      126—130
Dilogarithm of complex argument $\rm {Li}_{2}(r,\theta),$ functional equations, two variables      132
Dilogarithm of complex argument $\rm {Li}_{2}(r,\theta),$ special values, angle      131 137—139
Dilogarithm of complex argument $\rm {Li}_{2}(r,\theta),$ special values, argument      124—126
Eastham, M. S. P.      237 238
Edwards. J.      18 19 28 156
Erdelyi      28
Euler, L.      1 5 6 28 189
Euler, numbers      195
Feyer. W.      28
Finlayson, D.      35
Fletcher, A.      312
Fornberg, B.      314
Fuchs. W. H. J.      231
Functional equations      239
Generalized inverse tangent integral $\rm {Ti}_{2}(x,a),$ addition equation      96
Generalized inverse tangent integral $\rm {Ti}_{2}(x,a),$ definitions      41 68
Generalized inverse tangent integral $\rm {Ti}_{2}(x,a),$ derived relations      93 108
Generalized inverse tangent integral $\rm {Ti}_{2}(x,a),$ duplication formula      73 80 88
Generalized inverse tangent integral $\rm {Ti}_{2}(x,a),$ factorisation formula      89 90
Generalized inverse tangent integral $\rm {Ti}_{2}(x,a),$ form beyond singularity      83
Generalized inverse tangent integral $\rm {Ti}_{2}(x,a),$ form near singularity      72
Generalized inverse tangent integral $\rm {Ti}_{2}(x,a),$ interchange formula      71 78
Generalized inverse tangent integral $\rm {Ti}_{2}(x,a),$ inversion relation      75
Generalized inverse tangent integral $\rm {Ti}_{2}(x,a),$ multiplication formula      92
Generalized inverse tangent integral $\rm {Ti}_{2}(x,a),$ multivariate equations      76 79 84
Generalized inverse tangent integral $\rm {Ti}_{2}(x,a),$ relation to $\rm {Cl}_{2}$      107
Generalized inverse tangent integral $\rm {Ti}_{2}(x,a),$ special values      71 72 94
Generalized inverse tangent integral $\rm {Ti}_{2}(x,a),$ symmetry relation      68
Glaisher, J. W. L.      192 200 202 267—269
Golden-ratio integrals      232—235
hadamard      29
Hill, C. J.      1 9 18 28 29 69 102 110 120 121 176 258 259 312 355
Hoelder, O.      28 30 31
Hypergeometric function, relation to dilogarithm      30
Integrals from Coxeter's series      117 118
Inverse tangent integral $\rm {Ti}_{2}(x)$ duplication formula      40 42
Inverse tangent integral $\rm {Ti}_{2}(x)$ functional equation, several variables      59
Inverse tangent integral $\rm {Ti}_{2}(x)$ functional equation, two variables      62
Inverse tangent integral $\rm {Ti}_{2}(x)$ inversion relation      39
Inverse tangent integral $\rm {Ti}_{2}(x)$ multiplication formula      47
Inverse tangent integral $\rm {Ti}_{2}(x)$ numerical values      44 45 47 51
Inverse tangent integral $\rm {Ti}_{2}(x)$ quadruplication formulas      51—59
Inverse tangent integral $\rm {Ti}_{2}(x)$ relation to $\rm {Cl}_{2}$      106
Inverse tangent integral $\rm {Ti}_{2}(x)$ relation to ${\chi}_{2}$      38
Inverse tangent integral $\rm {Ti}_{2}(x)$ triplication formula      46
Jonquiere, A.      5 193 236
Kapteyn. W.      274
Koelbig, K. S.      314
Kuester, F.      237
Kummer's function $\Lambda$      199
Kummer, E. E.      5 9 10 13 16 28 33 102 114 120 121 122 123 136 137 142 152 154 166 175 177 178 181 182 184 186 187 193 199 206 209 213 216 238 239 312 355 356
Landen, J.      5 6 19 20 153 155 156 233
Laplace integrals      277
Laptev, B. L.      115
Legendre, ${\chi}_{2}$ function, definition      18
Legendre, ${\chi}_{2}$ function, integrals      256 274 275
Legendre, ${\chi}_{2}$ function, multiplication formula      20
Legendre, ${\chi}_{2}$ function, numerical values      19
Legendre, ${\chi}_{2}$ function, relation to ${Ti}_{2}$      38 49
Legendre, ${\chi}_{2}$ function, single variable equation      19
Legendre, A. M.      18 19 28 32
Leibniz. G. W.      336
Lerch's function      30
Lobacewskil space      35 115 118
Maier, W.      18 115
Mathematisch Centrum      28 313
Mitchell. K.      28 30 312
Muller, P. F.      115
Newman, F. W.      10 11 14 28 61 94 102 105 121 124 127 128 129 132 134 136 138 139 152 186 191 193 199 240 246 252 255 259 260 312 355
Nielsen, N.      5 10 18 21 22 28 29 45 120 122 153 227 265 266 267 274 349 355
Notation      1 27—29 39 121 145
Occurrence in physical problems      31—35 274 277
Pate. R. C      274
Phillip, J. R.      28 35
Picard, W. F.      236
Polylogarithm, absence of functional equations for n > 5      239
Polylogarithm, absence of recurrence relation      238
Polylogarithm, associated Clausen function      200
Polylogarithm, associated Clausen function, relation to Bn (a)      202
Polylogarithm, associated integrals      199
Polylogarithm, complex zeroes      314
Polylogarithm, definition      189
Polylogarithm, factorization formula      197
Polylogarithm, fifth order function      212
Polylogarithm, fifth order function, functional equation, single variable      213
Polylogarithm, fifth order function, functional equation, two variables      216
Polylogarithm, fifth order function, inversion relation      212
Polylogarithm, fourth order function      202
Polylogarithm, fourth order function, complex forms      205
Polylogarithm, fourth order function, functional equation, single variable      208
Polylogarithm, fourth order function, functional equation, two variables      211
Polylogarithm, fourth order function, generalized Clausen function      191 198
Polylogarithm, fourth order function, log sine integrals      205
Polylogarithm, fourth order function, log sine integrals, special values      206
Polylogarithm, fourth order function, numerical values      212
Polylogarithm, generating function      237
Polylogarithm, golden-ratio and related integrals      232—235
Polylogarithm, imaginary argument      190
Polylogarithm, inverse tangent integral      195
Polylogarithm, inversion relation      192
Polylogarithm, inversion relation for $\rm {Li}_{2}(r,\theta),$      196
Polylogarithm, Kummer's $\Lambda$ function      199
Polylogarithm, log sine integrals      191 192 200 216—232
Polylogarithm, log sine integrals, quasi periodicity      220
Polylogarithm, log sine integrals, special values      230
Polylogarithm, nonintegral order      34 236
Polylogarithm, nonintegral order, duplication formula      236
Polylogarithm, nonintegral order, inversion relation      236
Powell. E. O.      28 312
Ramanujan, S.      28 45
Relation of dilogarithm to other functions      30
Richmond      7 45
Rogers, L. J.      16 18 28 59 110 187 269 356
Sabri. A.      28 313
Sandham. H. F.      28 186 187 356
Sang, E.      28
Schaeffer, W.      9 10 28 176 177 260 262 263
Schlaeffli, L.      115 118
Schlomilch, O.      28
Sim, A. C      34
Spence, W.      5 8 9 28 32 39 40 43 69 86 90 94 95 122 137 138 139 140 142 154 172 173 177 181 193 195 259 263 265 271 312 349 355
Stieltjes. T. J.      267
Summation of series      237 260—269
Sylvester, J. J.      275
Szekeres. G.      7 145
Tabular values      34 102 312
Thomas, D. E.      313
Trigonometric integrals      253—260 274 278
Trigonometric integrals, special numerical values      276
Trilogarithm, complex forms      161 164 165 171 180 229
Trilogarithm, functional equations, for Rummer's ${\Lambda}_{3}$      184
Trilogarithm, functional equations, for several variables      187
Trilogarithm, functional equations, for single variable      155 161 178
Trilogarithm, functional equations, for two variables      173 177 186
Trilogarithm, functional equations, of Newman's type      185 186
Trilogarithm, generalization of Clausen's function      162
Trilogarithm, generalization of Clausen's function, factorization formula      163
Trilogarithm, generalization of Clausen's function, functional equation      180
Trilogarithm, generalization of Clausen's function, special values      163
Trilogarithm, inverse tangent integral      166
Trilogarithm, inversion relation      154
Trilogarithm, Legendre's ${\chi}_{3}$ function: special values      179
Trilogarithm, log sine integrals      165 169 272
Trilogarithm, numerical values      155 156 179
Trilogarithm, real part $\rm {Li}_{2}(r,\theta),$      167
Trilogarithm, real part $\rm {Li}_{2}(r,\theta),$ factorization formula      168
Trilogarithm, real part $\rm {Li}_{2}(r,\theta),$ inversion relation      168
Trilogarithm, real part $\rm {Li}_{2}(r,\theta),$ special angles      168
Trilogarithm, Rummer's function ${\Lambda}_{3}$, definition      165 182
Truesdell, C.      313
Van Wijngaarden      28 313
Watson, G. N.      145 146
Wechsung, G.      239
Wutzler, G.      18
Wynn, P.      34
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