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Forsyth A.R. — Theory of functions of a complex variable
Forsyth A.R. — Theory of functions of a complex variable

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Название: Theory of functions of a complex variable

Автор: Forsyth A.R.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1893

Количество страниц: 704

Добавлена в каталог: 31.08.2013

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Abbildung, conforme      11
Abel      456
Abelian transcendental functions, arising by inversion of functions of the first kind on a Riemann's surface      455
Abelian transcendental functions, Weierstrass's form of      456
Absoluter Betrag      3
Accidental singularities      16 53 64
Accidental singularities, are isolated points      65
Accidental singularities, form of function in vicinity of      64
Accidental singularities, if at infinity and there be no other singularity, the function is algebraical polynomial      69
Accidental singularities, if there be a finite number of, and no essential singularity, the uniform function is rational, algebraical and meromorphic      71
Accidental singularities, must be possessed by uniform function      64
Accidental singularities, number of, in an area      67 68 72
Accidental singularity      16 53
Addition-theorem, algebraical      297
Addition-theorem, algebraical, is possessed by algebraical functions      297
Addition-theorem, algebraical, is possessed by doubly-periodic functions      299
Addition-theorem, algebraical, is possessed by simply-periodic functions      298
Addition-theorem, condition that algebraical equation between three variables should express      310
Addition-theorem, definition of algebraical      297
Addition-theorem, for uneven doubly-periodic function of second order and second class      247
Addition-theorem, for Weierstrass's $\wp$-function      262
Addition-theorem, form of, when function is uniform      311
Addition-theorem, function which possesses an algebraical, is either (i) algebraical      300
Addition-theorem, function which possesses an algebraical, is or (ii) simply-periodic      303 305
Addition-theorem, function which possesses an algebraical, is or (iii) doubly-periodic      307
Addition-theorem, function which possesses an algebraical, is or (iii) doubly-periodic, satisfies a differential equation between itself and its first derivative      308
Addition-theorem, partial form of, for the $\sigma$-function and the $\zeta$-function      261
Addition-theorem, reference to binomial differential equations      490
Adelphic order      317
Algebraic (multiform) functions defined by algebraical equation      161
Algebraic (multiform) functions defined by algebraical equation, branch-points of      162 168
Algebraic (multiform) functions defined by algebraical equation, cyclical arrangements of branches round a branch-point      171
Algebraic (multiform) functions defined by algebraical equation, in connection, with Riemann's surface      338
Algebraic (multiform) functions defined by algebraical equation, infinities of, are singularities of the coefficients      163
Algebraic (multiform) functions defined by algebraical equation, infinities of, are singularities of the coefficients, graphical method for determination of order of      164
Algebraic (multiform) functions defined by algebraical equation, when all the branch-points are simple      174
Algebraic equation between three variables should express an addition-theorem, condition that      310
Algebraic equation, class of      349
Algebraic equation, defining algebraic multiform functions      161 see
Algebraic equation, for any uniform function of position on a Riemann's surface      371
Algebraic function on a Riemann's surface, integrals of      387
Algebraic function on a Riemann's surface, integrals of, branch-points of integrals of      393
Algebraic function on a Riemann's surface, integrals of, infinities of integrals of      390 393
Algebraic function on a Riemann's surface, integrals of, integrals of, everywhere finite      388
Algebraic function on a Riemann's surface, integrals of, integrals of, everywhere finite, number of, in a special case      388
Algebraic function on a Riemann's surface, integrals of, when all branch-points are simple, three kinds of integrals of      389
Algebraic function, rational integral      70
Algebraic functions on a Riemann's surface, constructed from normal elementary functions of second kind      457
Algebraic functions on a Riemann's surface, determine a fundamental equation for a given Riemann's surface      462
Algebraic functions on a Riemann's surface, relations between zeros and infinities of      468
Algebraic functions on a Riemann's surface, Riemann — Roch's theorem on      459
Algebraic functions on a Riemann's surface, smallest number of arbitrary infinities to render this construction possible      457
Algebraic functions on a Riemann's surface, smallest number of infinities of, which, except at them, is everywhere uniform and continuous      460
Algebraic functions on a Riemann's surface, which arise as first derivatives of functions of first kind      460
Algebraic functions on a Riemann's surface, which arise as first derivatives of functions of first kind, are infinite only at branch-points      460
Algebraic functions on a Riemann's surface, which arise as first derivatives of functions of first kind, determined by finite zeros      462
Algebraic functions on a Riemann's surface, which arise as first derivatives of functions of first kind, most general form of      461
Algebraic functions on a Riemann's surface, which arise as first derivatives of functions of first kind, number of infinities of, and zeros of      461
Algebraic isothermal curves, families of      576 see
Algebraic relation between functions automorphic for the same infinite group      653
Algebraic relation between functions automorphic for the same infinite group, class of, in general      654
Algebraical addition-theorem      297
Algebraical function determined by an equation      161
Algebraical function, rational      70
Amplitude      3
Analytic function, monogenic      56
Analytical curve      409 423 530
Analytical curve, area bounded by, represented on a half-plane      530
Analytical curve, area bounded by, represented on a half-plane, consecutive curve can be chosen at will      531
Analytical curve, represented on a circle      423
Analytical test of a branch-point      157
Anchor-ring conformally represented on plane      501
Anharmonic function, automorphic for the anharmonic group      620
Anharmonic group of linear substitutions      620
Anissimoff      111
Appell      145 295 296 464
Appell's factorial functions      464 see
Area, bounded by analytical curve represented on half-plane      530
Area, bounded by cardioid on half-plane      536
Area, bounded by circular arcs      549 see
Area, form of function for representation on a circle      529
Area, form of function for representation on a plane      528 540
Area, of convex rectilinear polygon      537 see
Area, simply connected, can be represented conformally upon a circle with unique correspondence of points, by Riemann's theorem      526
Areas, combination of, in proof of existence-theorem      425
Argand      2
Argument      3
Argument (or amplitude) of the variable      3
Argument and parameter of normal elementary function of third kind      453
Argument and parameter, interchange of      451
Argument of function possessing an addition-theorem, forms of, for a value of the function      300
Arithmetic mean, method of the      408
Ascoli      409
Ausserwesentliche singulaere Stelle      53
Automorphic function      619
Automorphic function, connection between, and general linear differential equations of second order      656
Automorphic function, constructed for infinite group in pseudo-automorphic form      638 see
Automorphic function, different, for same group are connected by algebraical equation      653
Automorphic function, different, for same group are connected by algebraical equation, class of this algebraical equation in general      654
Automorphic function, expressed as quotient of two thetafuchsian functions      651
Automorphic function, its essential singularities      651
Automorphic function, modular-functions as examples of      657
Automorphic function, number of irreducible zeros of, is the same as the number of irreducible accidental singularities      651
Automorphic functions      582 619
Barriers, can be used to classify connected surfaces      314
Barriers, changed into a cut      314
Barriers, impassable, in connected surface      313
Beltrami      530 532 533
Betrag, absoluter      3
Bianchi      617 618
Biehler      295
Bien defini      161
Biermann      55 297
Bifacial surface      325
Bifacial Surfaces      325 333
Binomial differential equations of first order when the integral is uniform, with the various classes of integrals      482
Bolza      583
Bonnet      500
Borchardt      218
Boundaries of connected surface, relation between number of, and connectivity      324
Boundary      322
Boundary conditions for potential function      410 see
Boundary of region of continuity of a function is composed of the singularities of the function      57
Boundary values of potential function for a circle      414
Boundary values of potential function for a circle, include all the maxima and the minima of a potential function      422
Boundary values of potential function for a circle, may have limited number of finite discontinuities      417
Boundary, assigned to every connected surface      314 322 329
Boundary, defined      322
Boundary, edges acquired by cross-cut and loop-cut      315
Boundary, effect of cross-cut on      323
Boundary, effect of cross-cut on, and of loop-cut on      324
Boundary, of simply connected surface is a single line      323
Branch      15
Branch-line      339
Branch-lines, are mode of junction of the sheets of Riemann's surfaces      339
Branch-lines, free ends of, are branch-points      340
Branch-lines, number of, when branch-points are simple      364
Branch-lines, properties of      340
Branch-lines, sequence along, how affected by branchpoints      341
Branch-lines, special form of, for two-sheeted surface      344
Branch-lines, special form of, for two-sheeted surface, when all branch-points are simple      356
Branch-lines, system of, for a surface      341
Branch-point      15 154
Branch-points, analytical test of      157
Branch-points, are free ends of branch-lines      340
Branch-points, canonical arrangement of, when simple      364
Branch-points, circuits round two, are irreducible      350
Branch-points, defined      15 154
Branch-points, deformation of circuit on Riemann's surface over, is impossible      350
Branch-points, effect of, on branches      149 151
Branch-points, effect of, on sequence of interchange along branch-lines      341
Branch-points, expression of branches of a function in vicinity of      158
Branch-points, in connection with loops      357 see
Branch-points, integral of a function round any curve containing all the      37
Branch-points, joined by branch-lines when simple      344
Branch-points, number of simple      175
Branch-points, number of, when simple      356
Branch-points, of algebraic functions      162 168
Branch-points, simple      174 355
Branch-section      339
Branches of a function, a function which has a limited number of, is a root of an algebraic equation      175
Branches of a function, affected by branch-points      151
Branches of a function, analytical expression of, in vicinity of branch-point      158
Branches of a function, are uniform in continuous regions where branch-points do not occur      155
Branches of a function, defined      15
Branches of a function, number of, considered      159
Branches of a function, obtained by continuation      151
Branches of a function, of an algebraic function      161 see
Branches of a function, restored after number of descriptions of circuit round branch-point      157
Branches of a function, which are affected by a branch-point, can be arranged in cycles      156
Brill      356 367 464
Brioschi      275 281
Briot      456 464
Briot and Bouquet      vii 23 39 41 168 173 208 210 218 230 456 482 489 490
Burnside (W.)      117 247 355 406 524 536 558 620 640 654
Burnside (W.S.) and Panton      390
Canonical form of complete system of simple loops      361
Canonical form of complete system of simple loops, Riemann's surface      365
Canonical form of complete system of simple loops, Riemann's surface, resolved      366
Canonical resolution of Riemann's surface      355
Canonical resolution of surface      355
Cantor      147
Cardioid, area bounded by, on a circle      536
Cardioid, area bounded by, represented on strip of plane      535
Casorati      2 23 359
Categories of corners      592 see
Categories of corners, cycles      592 596
Cathcart      6
Cauchy      v vii 23 27 43 51 61 180 312
Cauchy's theorem on the integration of a holo-morphic function round a simple curve      23
Cauchy's theorem on the integration of a holo-morphic function round a simple curve and of a meromorphic function      27
Cauchy's theorem on the integration of a holo-morphic function round a simple curve on the expansion of a function in the vicinity of an ordinary point      43
Cayley      2 11 74 356 476 482 509 510 515 529 530 533 537 549 575 576 579 620 622
Cesaro      92
Christoffel      538 541 549
Chrystal      vi 2 6 48 170 184
Circle, areas of curves represented on area of, any circle, by properly chosen linear substitution      514
Circle, areas of curves represented on area of, any simply connected area, by Riemann's theorem      526
Circle, areas of curves represented on area of, exterior of ellipse      501
Circle, areas of curves represented on area of, exterior of parabola      505
Circle, areas of curves represented on area of, exterior of square      545
Circle, areas of curves represented on area of, half-plane      506
Circle, areas of curves represented on area of, infinitely long strip of plane      508
Circle, areas of curves represented on area of, interior of cardioid      536
Circle, areas of curves represented on area of, interior of ellipse      504
Circle, areas of curves represented on area of, interior of parabola      506
Circle, areas of curves represented on area of, interior of rectangle      502 544
Circle, areas of curves represented on area of, interior of regular polygon      548 (Ex.)
Circle, areas of curves represented on area of, interior of semicircle      507
Circle, areas of curves represented on area of, interior of square      503 545
Circle, discriminating      111
Circuit      327
Circuits, cannot be deformed over a branch-point on a Riemann's surface      350
Circuits, complete system of, contains unique number of circuits      328
Circuits, drawn on a simply connected surface are reducible      329
Circuits, number in complete system for multiply connected surface      330
Circuits, on connected surface      327
Circuits, reducible, irreducible, simple, multiple, compound, reconcileable      327
Circuits, represented algebraically      328
Circuits, restore initial branch after number of descriptions      157
Circuits, round branch-point, effect of, on branch of a function      153 155
Circular functions obtained, by integrating algebraical functions      191
Circular functions obtained, on a Riemann's surface      380
Class (of connected surface)      324
Class of doubly-periodic function of second order      223
Class of equation      349
Class of group      608
Class of singularity      147
Class of tertiary-periodic function      288
Class of transcendental integral functions      89
Class of, algebraic equation associated with a Riemann's surface      349
Class of, algebraic equation associated with a Riemann's surface, between automorphic functions      654
Class of, connected surface      324
Class of, essential singularity      147
Class of, Fuchsian group      608
Class of, Laguerre's criterion of      91
Class of, Riemann's surface      349
Class of, simple function of given class      91
Class of, tertiary-periodic function, negative      291
Class of, tertiary-periodic function, positive      288
Class of, transcendental integral function, as defined by its zeros      89
Classes of doubly-periodic functions of the second order are two      223
Clebsch      174 209 356 359 361 363 364 367 403 455 456
Clifford      333 361
Closed cycles of corners in normal polygon for division of plane      596 see
Combination of areas      425
Combination of areas, in determination of potential function      425
Complex variable defined      1
Complex variable defined, represented on a plane      2
Complex variable defined, represented on a plane, and on Neumann's sphere      4
Compound circuit      327
Compound circuits      327
Conditions that one complex variable be a function of another      7
Conformal representation      11
Conformal representation of planes, established by functional relation between variables      11
Conformal representation of planes, examples of      501
Conformal representation of planes, magnification in      11
Conformal representation of planes, most general form of relation that secures, is relation between complex variables      496
Conformal representation of planes, used in Schwarz's proof of existence-theorem      423
Conformal representation of surfaces is secured by relation between complex variables in the most general manner      492
Conformal representation of surfaces is secured by relation between complex variables in the most general manner, form of function for, on a circle      529
Conformal representation of surfaces is secured by relation between complex variables in the most general manner, form of function for, on a plane      528
Conformal representation of surfaces is secured by relation between complex variables in the most general manner, obtained by making one a plane      495
Conformal representation of surfaces is secured by relation between complex variables in the most general manner, of anchor-ring      501
Conformal representation of surfaces is secured by relation between complex variables in the most general manner, of ellipsoid      500
Conformal representation of surfaces is secured by relation between complex variables in the most general manner, of oblate spheroid      500
Conformal representation of surfaces is secured by relation between complex variables in the most general manner, of sphere on plane      497
Conformal representation of surfaces is secured by relation between complex variables in the most general manner, of sphere on plane, Mercator's and stereographic projection      498
Conformal representation of surfaces is secured by relation between complex variables in the most general manner, of surfaces of revolution on plane      496
Conformal representation of surfaces is secured by relation between complex variables in the most general manner, Riemann's general theorem on      526
Conforme Abbildung      11
Congruent figures      517 591
Congruent regions by linear substitutions      517 591
Conjugate edges      592
Conjugate edges of a region      592 see
Connected surface      312
Connected surface, can be deformed into any other connected surface of the same connectivity having the same number of boundaries, if both be bifacial      334
Connected surface, divided into polygons, Lhuilier's theorem on      325
Connected surface, geometrical and physical deformation of      333
Connected surface, Klein's normal form of      334
Connected surface, supposed to have a boundary      314 322 329
Connected surface, to be bifacial      325
Connection of surfaces, affected by cross-cuts      319
Connection of surfaces, affected by cross-cuts, and by slit      321
Connection of surfaces, affected by cross-cuts, by loop-cuts      320
Connection of surfaces, defined      312
Connection of surfaces, multiple      314
Connection of surfaces, multiple, definition of      315
Connection of surfaces, simple      313
Connection of surfaces, simple, definition of      315
Connection, order of      317
Connectivity      317
Connectivity, affected by cross-cuts      319
Connectivity, affected by cross-cuts, by loop-cuts      320
Connectivity, affected by cross-cuts, by slit      321
Connectivity, in relation to irreducible circuits      330
Connectivity, of a Riemann's surface, with one boundary      347
Connectivity, of a Riemann's surface, with one boundary, with several boundaries      350
Connectivity, of spherical surface with holes      321
Connectivity, of surface defined      317
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