Электронная библиотека Попечительского советамеханико-математического факультета Московского государственного университета
 Главная    Ex Libris    Книги    Журналы    Статьи    Серии    Каталог    Wanted    Загрузка    ХудЛит    Справка    Поиск по индексам    Поиск    Форум Авторизация Поиск по указателям     Macrobert T.M. — Functions of a complex variable Обсудите книгу на научном форуме Нашли опечатку?Выделите ее мышкой и нажмите Ctrl+Enter Название: Functions of a complex variable Автор: Macrobert T.M. Язык: Рубрика: Математика/ Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Издание: 5-th edition Год издания: 1962 Количество страниц: 436 Добавлена в каталог: 25.11.2012 Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID Предметный указатель -plane      10 -plane      2 10 Abel’s test for convergence of series      80 Abel’s theorem on continuity of series      125 Addition of complex numbers      1 3 Amplitude      2 4 Amplitude, of a function, variation of      11—17 Amplitude, principal value of      2 4 Argand diagram      2 Argument      2 Asymptotic expansions      136; see Bessel E-functions Euler Gamma Kummer Whittaker Barnes Integrals      151 374 Bernoulli numbers      132 328 402 Bessel function      236 Bessel function 240 Bessel function , addition theorem for      254 Bessel function , asymptotic expansion of      273 Bessel function , in terms of Bessel functions of first and second kinds      240 Bessel function , recurrence formulae for      241 Bessel function of Becond kind      238 239 Bessel function of first kind      237 Bessel function of first kind, addition theorem for      254 Bessel function of first kind, as a contour integral      267 268 270 Bessel function of first kind, as a function of its order      239 320 Bessel function of first kind, asymptotic expansions of      273 274 Bessel function of first kind, products of      340 Bessel function of first kind, recurrence formulae for      239 Bessel function of first kind, zeros of      241 274 Bessel functions, modified      267—270 347 351 Bessel functions, modified, asymptotic expansions of      271 293 Bessel functions, relations between      241 Bessel functions, relations between, Lommel integrals, for      321 Bessel’s equation      236 266 Bessel’s transformed equation      267 beta function      144 145 Binomial theorem      90 Branch of function      13 Branch point      14 39 Branch point, of an integral      257 Cauchy’s integral theorem      61 54 Cauchy’s integral theorem, integral      321 Cauchy’s integral theorem, residue theorem      57 Circular functions      33 83 90 Coefficients, undetermined      96 Collineanty of points on cubic      197 complex numbers      1 Complex numbers, geometrical representation of      1 Complex numbers, operations with      1—5 Complex variable      7 Complex variable, function of a      7 Complex variable, path of variation of a      7 Confluent hypergeometrio function      348 Conformal representation      37 370 Congruent points      179 180 Conjugate numbers      1 2 connected region      30 Continuation, analytical      122 208 350 Continuation, analytical, of hypergeometrio function      153 156 249 297—301 370 371 Continuation, analytical, of integral of differential equation      213 Continuation, analytical, theorems on      123 124 Continuity      23 24 Continuity, Abel’s theorem on      125 Continuity, of series      92 Continuity, uniform      24—26 Convergence of infinite product      107 108 Convergence of infinite product, unconditional      107 Convergence of sequence      42 Convergence of sequence, uniform      42 Convergence of series      76 Convergence of series, absolute      76 78 358 359 Convergence of series, circle of      80 Convergence, of a double aeries      78 Convergence, of power series      80 82 95 358 359 360 Convergence, radius of      80 Convergence, ratio tests for      77 Convergence, uniform      92 347 348 Coordinates, polar      2 29 294 Coordinates, polar, rectangular      2 Cross-cut      30 Cylindrical functions      236 Derivative      26 28 Derivative, of function of a function      30 Derivative, of holomorphic function      28 70 Derivative, of inverse function      30 Derivative, partial      31 70 Determinant of fundamental system      216 223 Determinant of fundamental system, index of      224 Differential equation, homogeneous linear      209 Differential equation, homogeneous linear, coefficients of      210 Differential equation, homogeneous linear, construction of      216 Differential equation, homogeneous linear, domain of ordinary point of      210 Differential equation, homogeneous linear, dominant equation      210 Differential equation, homogeneous linear, Frobenius’ method of solution      225 Differential equation, homogeneous linear, fundamental equation      220 Differential equation, homogeneous linear, fundamental system      215 257 Differential equation, homogeneous linear, indicial equation      225 Differential equation, homogeneous linear, integrals of      210 Differential equation, homogeneous linear, of the first order      210 Differential equation, homogeneous linear, of the second order      210 Differential equation, homogeneous linear, ordinary point of      210 Differential equation, homogeneous linear, singularity of      210 Differential equation, homogeneous linear, solutions of      210 Differentiation      26 28 29 Differentiation, of series      93 Differentiation, under integral sign      44 69 138 Discontinuity, removable      23 Division of complex numbers      1 4 Dixon’s theorem      362 Domain of a point      38 210 Dougall's theorems      371 372 E-functions      348 352 393—397 404 15 E-functions, asymptotic expansions of      351 358 E-functions, Barnes integral for      374 Elements of a function      208 Elliptic function      180 Elliptic function, order of      181 182 Elliptic function, poles of      180—183 Elliptic function, zeros of      182; see Jacobian and Weierstrassian functions Elliptic integrals      169 Elliptic integrals, reduction of      170—173 Elliptic integrals, transformation of      170—174 295 Equation, roots of      16 69 363 Euler’s constant      135 Euler’s constant, asymptotic expansion of      134 Euler’s definition of gamma function      141 Euler’s numbers      328 402 Evaluation of 329 Expansion of functions in series of fractions      103 105 115 116 326 Expansion, Lagrange’s      119 Exponential function      32 90 Ferrers’ function      307 Fourier series      86 Fourier — Beesel integral theorem      321 383 Fourier’s integral theorem      319 323 340 341 Fresnel integrals      62 Frobenius’ method of solving linear differential equations      225 Frobenius’ method of solving linear differential equations, indicial equation      225 Frobenius’ method of solving linear differential equations, solutions free from logarithms      228 Frobenius’ method of solving linear differential equations, uniform convergence of series with regard to index      227 Fuchsian type, equations of      243 Fuchsian type, equations of, sum of indices a constant      243 244 Function, analytic      29 208 Function, analytic, conjugate      31 Function, analytic, continuous      23 Function, analytic, dominant      210 Function, analytic, doubly-periodic      179 Function, analytic, elements of a      208 Function, analytic, even      33 97 Function, analytic, geometrical representation of a      7 10 Function, analytic, holomorphic      29 52 93 294 Function, analytic, initial value of      10 Function, analytic, integral      88 Function, analytic, integrals of      48 Function, analytic, inverse      30 Function, analytic, limit of      22 Function, meromorphic      39 40 89 160 Function, multiform or multiple-valued      7 161 209 Function, odd      33 97 Function, of a complex variable      7 Function, of a function      24 30 49 Function, of two complex variables      69 137 Function, of two real variables      26 Function, periodic      32 86 Function, periodic, of the second kind      187 Function, periodic, of the third kind      189 Function, rational      89 Function, rational integral      88 Function, region of existence of      7 Function, regular      29 Function, simply-periodic      86 Function, single-valued      7 209 Function, transcendental integral      88 Function, uniform      7 209 Function, uniform, classification of      88 Fundamental equation      220 Fundamental system of integrals      210 257 Fundamental system of integrals, associated with fundamental equation      220 Fundamental system of integrals, in neighbourhood of singularity      219 Fundamental theorem of algebra      68 69 Gamma function      67 75 109 139 141 Gamma function, asymptotic expansion of      146 374 Gamma function, duplication formula for      145 Gamma function, Euler’s definition of      141 Gamma function, expression as a contour integral      143 Gamma function, Gauss’s definition of      141 Gamma function, the derived function 141 Gauss’s differential equation      228 258 Gauss’s differential equation, function 141 Gauss’s differential equation, sum      117 Gauss’s differential equation, theorem      144 275 Generalised hypergeometric functions      343 358 Generalised hypergeometric functions, expressed as multiple series      363 Geometrical representation      see Complex numbers Functions Green’s Theorem      45 Gregory’s aeries      84 Harmonic functions      31 Hyperbolic functions      33 90 Hypergeometric equation      228 258 Hypergeometric equation, relations between integrals of      249 298 Hypergeometric equation, the twenty-four integrals of      247 297 Hypergeometric function      77 151 229 246 247 297 298 Hypergeometric function, analytical continuation of      153 156 249 297—301 Hypergeometric function, as a contour integral      259 Hypergeometric function, asymptotic expansion of      301 Hypergeometric function, confluent      348 Hypergeometric function, generalised      343 358 Hypergeometric series      77 78 144 Hypergeometric series, convergence of      77 I( ) notation      1 identities      83 Image of point      9 Indented contour      65 Indicial equation      225 Indicial equation, fundamental system      227 Infinity, point at      9 Infinity, point at, continuity at      23 Infinity, point at, integral at      51 137 139 Infinity, point at, integrals of differential equations at      212 213 224 Infinity, point at, loop about      162 168 Infinity, point at, residue at      58 96 Infinity, point at, singularity at      38 39 Integrals of differential equation      210 Integrals of differential equation, analytical continuation of      213 Integrals of differential equation, at infinity      212 213 Integrals of differential equation, existence of      210 Integrals of differential equation, existence of, fundamental system of      215 Integrals of differential equation, existence of, in form of infinite series      213 Integrals of differential equation, existence of, initial values of      210 Integrals of differential equation, existence of, lineally independent      215 Integrals of differential equations in form of definite integrals      255 266 Integrals of differential equations in form of definite integrals, branch points of      257 Integrals of differential equations in form of definite integrals, fundamental system of      257 Integrals of differential equations near a singularity      219 Integrals of differential equations near a singularity, at infinity      224 Integrals of differential equations near a singularity, fundamental system of      219 Integrals of differential equations near a singularity, index of      222 Integrals of differential equations near a singularity, regular      222 Integrals, contour      59 97 113 Integrals, contour, convergent      136 Integrals, contour, curvilinear      42 Integrals, contour, definite      48 Integrals, contour, double      69 138 Integrals, contour, elliptic      169 Integrals, contour, evaluation of definite      59 97 113 Integrals, contour, finite moduli of definite      50 Integrals, contour, Fresnel      62 Integrals, contour, indefinite      53 Integrals, contour, independent of paths      52 Integrals, contour, limiting values of definite      60 63 113 115 Integrals, contour, of holomorphic functions      50—52 Integrals, contour, of meromorphic functions      160 Integrals, contour, of multiform functions      161 Integrals, contour, principal values of      65 323 Integrals, contour, uniformly convergent      137 Integrals, contour, with infinite paths      51 137 139 Integrand, infinite      136 139 Integration, change of order of      69 138 Integration, change of order of, of series      93 Integration, change of order of, partial      53 Integration, change of order of, under integral sign      69 138 Invariants      see Weierstrass Inverse points      9 Inverse sine function      163 Inverse tangent function      34 84 86 Jacobian elliptic functions      167 182 198 Jacobian elliptic functions, addition theorems for      202 Jacobian elliptic functions, complementary modulus of      166 167 200 Jacobian elliptic functions, derivatives of      200 Jacobian elliptic functions, differential equations of quarter periods of      176 231 Jacobian elliptic functions, duplication formulae for      204 Jacobian elliptic functions, Legendre’s relation for      175 Jacobian elliptic functions, moduli of      167 200 Jacobian elliptic functions, orders of      182 202 Jacobian elliptic functions, periods of      167 201 202 Jacobian elliptic functions, poles of      200 202 Jacobian elliptic functions, relation to Weierstrassian functions      201 Jacobian elliptic functions, relations between      200 Jacobian elliptic functions, relations between periods of      202 Jacobian elliptic functions, residues at poles of      202 205 Jacobian elliptic functions, transition from Weierstrassian function to      198 Jacobian elliptic functions, zeros of      200 Jacobi’s imaginary transformation      205 Kummer’s function      346 Kummer’s function, asymptotic expansion of      350 Lagrange’s expansion      119 125 Landen’s transformation      174 Laplace’s equation      31 Laurent’s series      84 95 Laurent’s series, absolute convergence of      85 Legendre functions      234 Legendre functions, addition theorems for      314—318 333 Legendre functions, of the first kind      214 235 236 Legendre functions, of the second kind      235 236 Legendre functions, recurrence formulae for      236 252 289 290 310 Legendre polynomials      99 214 235 Legendre polynomials, expression in series      102 103 121 Legendre polynomials, in definite integral forms      100—102 Legendre polynomials, integrals involving      122 Legendre polynomials, recurrence formulae for      102 124 129 Legendre polynomials, Rodrigues’ formula for      120
1 2 Реклама     © Электронная библиотека попечительского совета мехмата МГУ, 2004-2022 | | О проекте