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Knopp K. — Theory of functions

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Название: Theory of functions

Автор: Knopp K.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1947

Количество страниц: 160

Добавлена в каталог: 25.11.2012

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 branch-point      143
Algebraic configuration      134
Algebraic curve      84
Algebraic differential equation      72 82
Algebraic functions      x 119—134
Algebraic point      131
Algebraic relation      71
Algebraic singularity      x 131 143
Analytic configuration      x 135—146
Analytic continuation      93ff.
Analytic function, monogenic      135—139
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 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
Element of a function      141
Elementary functions      vii
Elliptic functions      ix 73—92
Elliptic integral      85
Entire functions      viii 1—33
Entire functions with no zeros      3
Euler's constant      32
Eulerian gamma-function      31 48—51
Eulerian integral      31
Factor-theorem      see "Weierstrass"
Factors, convergence-producing      18
Factors, primary      18
Functional element      141
Functional 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
Functions, multiple-valued      ix 93—146
Functions, rational      viii ix 1 34 35
Functions, simply periodic      ix 64—72
Functions, single-valued      1—92
Fundamental parallelogram      73
Fundamental 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 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—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
Meromorphic functions      ix 34—57
Mittag-Leffier's partial-fractions-theorem      34—40
Mittag-Leffier's partial-fractions-theorem, applications of      42—57
Mittag-Leffier's partial-fractions-theorem, proof of      39—42
Monogenic analytic function      135—139
Multiple-valued functions      ix 93—146
Network of parallelograms      27 73
Order of a branch-point      103ff.
Order of an elliptic function      75
Pair of periods      63
Parallelogram network      27 73
Parallelogram, fundamental      73
Partial-fractions decomposition      34
Partial-fractions decomposition of $\pi\ cot\ \pi z$       43 44
Partial-fractions decomposition of $\wp(z)$       45—47
Partial-fractions decomposition of meromorphic 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, 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 representation of $1/\Gamma(z)$       30—33
Product representation of $sin\ \pi z$       23—27
Product representation of $\sigma(z)$       27—30
Product representation of entire functions      2 7
Product, Wallis's      33 50
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 convergence of infinite products      11
Region of existence      94
Regular point      93
Representation of functions by means of products      11
Riemann spherical surface      105
Riemann surface      93—118 139—142
Riemann surface for $\sqrt[p]{z}$       104—106
Riemann surface for $\sqrt{(z-a_{1})\cdot\cdot\cdot(z-a_{k})}$       112—117
Riemann surface for $\sqrt{z}$       100—104
Riemann surface for log z      106—110
Riemann 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
Weierstrass's $\wp$ -function      45—47 78—92
Weierstrass's factor-theorem      6 18
Weierstrass's factor-theorem, applications of      22—33
Weierstrass's factor-theorem, proof of      16—22
Weierstrass's sigma-function      27—30 86—92
Weierstrass's zeta-function      46
Weierstrassian theory of elliptic functions      82
Zeta-function of Riemann      46 51—55
Zeta-function of Weierstrass      46

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