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

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Íàçâàíèå: Theory of functions of a complex variable

Àâòîð: Forsyth A.R.

ßçûê:

Ðóáðèêà: Ìàòåìàòèêà/

Ñòàòóñ ïðåäìåòíîãî óêàçàòåëÿ: Ãîòîâ óêàçàòåëü ñ íîìåðàìè ñòðàíèö

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Ãîä èçäàíèÿ: 1893

Êîëè÷åñòâî ñòðàíèö: 704

Äîáàâëåíà â êàòàëîã: 31.08.2013

Îïåðàöèè: Ïîëîæèòü íà ïîëêó | Ñêîïèðîâàòü ññûëêó äëÿ ôîðóìà | Ñêîïèðîâàòü ID
Ïðåäìåòíûé óêàçàòåëü
 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 -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 -function and the -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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