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Knopp K. — Theory of Functions. Part Two

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Название: Theory of Functions. Part Two

Автор: Knopp K.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1947

Количество страниц: 155

Добавлена в каталог: 05.07.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

$\Sigma$ -function      27—30 86—92
$\wp$ -function      45—47 78—92
Abel      74 85
Absolute convergence of infinite products      9
Addition-theorem      71 88
Algebraic addition-theorem      71 88
Algebraic addition-theorem branch-point      143
Algebraic addition-theorem configuration      134
Algebraic addition-theorem curve      84
Algebraic addition-theorem differential equation      72 82
Algebraic addition-theorem elation      71
Algebraic addition-theorem functions, x      119—134
Algebraic addition-theorem point      131
Algebraic addition-theorem singularity, x      131 143
Analytic configuration, continuation      93ff.
Analytic configuration, function, monogenic      135—139
Analytic configuration, x      135 146
Asymptotically equivalent      50
Bank of a cut      101
Branch      100 104 141
Branch-point      103—108 143
Branch-point of infinite order      108
Branch-point, simple      103
C (Euler’s constant)      32
Configuration, algebraic      134
Configuration, analytic, x      135—146
Conformal mapping      106
Congruent points      65
Continuity of the roots      122
Continuous mapping      106
Convergence of infinite products      8
Convergence of infinite products in the stricter sense      8
Convergence-producing factors      18
Convergence-producing factors terms      42
Curve, algebraic      84
CYCLE      128
Derivative, logarithmic      14
Differentiability of the roots      125
Differential equation, algebraic      72 82
Discriminant      120
Doubly periodic functions, ix      63 73—92
Elementary functions, vii Element of a function      141
Elliptic functions      ix 73—92
Elliptic functions, integral      85
Entire functions      viii 1—33
Entire functions with no zeros      3
Eulerian gamma-function      31 48—51
Eulerian gamma-function, integral      31
Euler’s constant      32
Factor-theorem      (see Weier-s trass)
Factors, convergence-producing      18
Factors, primary      18
Functional element      141
Functional element, equation      48
Functions, algebraic      x 119 134
Functions, doubly periodic, ix      73—92
Functions, elementary      vii
Functions, elliptic      ix 73—92 74
Functions, entire      viii 1—33
Functions, meromorphic      ix 34—57
Functions, monogenic analytic      135—139 146
Functions, rational      viii ix 35
Functions, simply periodic      ix 64 72
Functions, single-valued      1—92
Fundamental parallelogram      73
Fundamental parallelogram, theorem of algebra      1 112
Gamma-function      31 48—51
Gauss      31
Genus      116 117
Helicoid      102
Invariants of the $\wp$ -function      82
Inverse configuration      145
Inverse configuration, function      85
Inversion of an integral      72 85
Inversion problem      85
Irreducible      120
jacobi      74 82 85
Koebe      146
Lattice points      27
Laurent expansions      128 129 130 143 144

Liouville theorems      74—78
Logarithm      93—118
Logarithmic derivative      14
Mapping      106
Mapping, conformal      106
Mapping, continuous      106
Mascheroni’s constant      32
Meromorphie functions, ix      34—57
Mittag — Leffler’s partial-fractions-theorem      34—39 40
Mittag — Leffler’s partial-fractions-theorem, proof of      39—42
Mittag — Leffler’s, applications of      42—57
Monogenic analytic function      135—139
Multiple-valued functions      ix 93—146 149
Network of parallelograms      27 73
Order of a branch-point      103ff.
Order of a branch-point an elliptic function      75
Pair of periods      63
Parallelogram, fundamental      73
Parallelogram, network      27 73
Partial-fractions decomposition      34
Partial-fractions decomposition of $\pi cot \pi \textit{z}$       43 44
Partial-fractions decomposition of $\wp(z)$       45—47
Partial-fractions of meromorphie functions      38
Partial-fractions theorem      (see Mittag-Leffler)
Period-point      59
Period-point, -ratio      63 64
Period-strips      65
Periodic functions      58—92
Periods of analytic functions      58—64
Periods of analytic functions, primitive      61
Permutation      128
Poincare      146
Point, congruent      65
Point, regular      93
Point, singular      141
Pole      143
Primary factors      18
Primitive periods      61
Primitive periods, pair of      63
Principal part      34
Pringsheim      31
Product, Wallis’s      33 50
Product, Wallis’s of $l/\Gamma(z)$       30—33
Product, Wallis’s of $sin \pi \textit{z}$       23—27
Product, Wallis’s of $\sigma(\textit{z})$       27—30
Product, Wallis’s representation of entire functions      2 7
Products, infinite      7—16
Punctured plane      121
Rational functions      viii ix 1 34 35
Rational functions of $e^{2\pi iz}$       70—72
Region of existence      94
Region of existence convergence of infinite products      11
Regular point      93
Representation of functions by means of products      11
Riemaim spherical surface      105
Riemaim spherical surface for $\sqrt[p]{z}$       104—106
Riemaim spherical surface for $\sqrt{(z-a_{1})\cdot\cdot\cdot(z-a_{k})}$       112—117
Riemaim spherical surface for $\sqrt{z}$       100—104
Riemaim spherical surface for log z      106—110
Riemaim spherical surface, surface      93—118 139—1 42
Riemaim spherical surface, zeta-function      46 51—55
Root      93—118
Rouche’s Theorem      111
Sheet      140
Simply periodic functions      ix 61 64—72
Single-valued functions      1—92
Singular point      141
Singularity, algebraic      x 131 143
Surfaces, Riemann      93—118 139—142
Uniformization      84 145
Wallis’s product      33 50
Weierstrassian theory of elliptic functions      82
Weierstrass’s factor-theorem      6 18
Weierstrass’s factor-theorem, $\wp$ -funetion      45—47 78—92
Weierstrass’s factor-theorem, applications of      22—33
Weierstrass’s factor-theorem, proof of      16—22
Weierstrass’s factor-theorem, sigma-funetion      27—30 86—92
Weierstrass’s factor-theorem, zeta-function      4
Zeta-function of Riemann      46 51—55
Zeta-function of Riemann of Weierstrass      46

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