Abstract
F -DISTRIBUTION — See Fisher F -distribution. AMS 1980 Subject Classification: 62EXX
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References
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SUETIN, P.K.: ‘Series in Faber polynomials and several generalizations’, J. Soviet Math. 5 (1976), 502–551.Itogi Nauk. i Tekhn. Sovr. Probl. Mat.5 (1975), 73–140).
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GAIER, D.: Vorlesungen über Approximation im Komplexen, Birkhäuser, 1980.
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SEMADENI, Z.: Schauder bases in Banach spaces of continuous function, Springer, 1982.
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LANDAU, E.: ‘Darstellung und Begründung einiger neurer Ergebnisse der Funktionentheorie’, in Das Kontinuum und andere Monographien,Chelsea, reprint, 1973.
DIENES, P.: The Taylor series, Oxford Univ. Press & Dover, 1957.
PEDERSEN, G.K.: C-algebras and their automorphism group, Acad. Press, 1979.
DIXMIER, J.: C-algebras, North-Holland, 1977 (translated from the French).
HARMAN, H.H.: Modern factor analysis, Univ. of Chicage Press, 1976.
AĭVAZYAN, S.A., BEZHAEVA, Z.I. and STAROVEROV, O.V.: The classification of multi-dimensional observations, Moscow, 1974 (in Russian).
SPEARMAN, C.: Amer. J. Psychology 15 (1974), 201–293.
ANDERSON, T.W. and RUBIN, H.: ‘Statistical inference in factor analysis’, Proc, 3 rd Berkeley Symp. Math Statist., Vol. 5, Univ. California Press, 1956, pp. 111–150.
RAO, C.R.: ‘Estimation and tests of significance in factor analysis’, Psychometrika 20 (1955), 93 - 111.
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EVERITT, B.S.: An introduction to latent variable methods, Chapman & Hall, 1984.
BOURBAKI, N.: Elements of mathematics. Commutative algebra, Addison-Wesley, 1972 (translated from the French).
HARARY, F.: Graph theory, Addison-Wesley, 1969, Chapt. 9.
PETERSEN, J.: ‘Die theorie der regularen Graphen’, Acta. Math. 15 (1891), 193–220.
TUTTE, W.T.: ‘Graph’factors’, Combinatorica 1 (1981), 79–97.
AKIYAMA, J. and KANO, M.: ‘Factors and factorizations of graphs — a survey’, J. Graph Theory 9 (1985), 1–42.
SPITZER, F.: Principles of random walk, Springer, 1976.
BOROVKOV, A.A.: Stochastic processes in queueing theory, Springer, 1976 (translated from the Russian).
GIHMAN, I.I. [I.I. Gikhman] and Skorohod, A.V.: The theory of stochastic processes, 1, Springer, 1971, Chapt. 4, Sect. 7 (translated from the Russian).
FISCHER, R.A.: ‘On the mathematical foundations of theoretical statistics’, Philos. Trans. Roy. Soc. London Ser. A 222 (1922), 309–368.
NEYMAN, J.: ‘Su un teorema concernente le cosiddette statis- tiche sufficienti’, Giorn. Istit. Ital. Att. 6 (1935), 320–334.
LEHMANN, E.L.: Testing statistical hypotheses, Wiley, 1959.
IBRAGIMOV, LA. and Has’minskii, R.Z. [R.Z. Khas’minskiĭ]: Statistical estimation: asymptotic theory, Springer, 1981 (translated from the Russian).
HALMOS, P.R. and SAVAGE, L.J.: ‘Application of the Radon—Nikodym theorem to the theory of sufficient statistics’, Ann. of Math. Statist. 20 (1949), 225–241.
COX, D.R. and HINKLEY, D.V.: Theoretical statistics, Chapman & Hall, 1974, p. 21.
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SCHMID, E. and ZIEGELMANN, H. The quantum-mechanical three-body problem, Braunschweig, 1974.
FERREIRA, et al. (eds.): Models and methods in few body physics. Proc. Lisboa 1986, Springer.
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Few body systems in particle and nuclear physics. Proc. 11th Conf. Tokyo, August 1986’, Nuclear Physics A 463, no. 1–2 (1987).
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TROELSTRA, A.S.: Choice sequences, Clarendon Press, 1977.
COXETER, H.S.M.: Introduction to geometry, Wiley, 1961.
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Izv. Akad. Nauk SSSR Ser. Mat.34, no. 6 (1970), 1200–1208)
CLEMENS, C. and GRIFFITHS, P.: ‘The intermediate Jacobian of the cubic threefold’, Ann. of Math. 95 (1972), 281–356.
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FANO, G.: ‘Si alcune varietà algebriche a tre dimensioni razionali, e aventi curve-sezioni canoniche’, Comment. Math. Helv. 14 (1942), 202–211.
MORI, S. and MUKAI, S.: ‘Classification of Fano 3-folds with B2≥2’, Manuscripta Math. 36, no. 2 (1981), 147–162.
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ISKOVSKIKH, V.A.: ‘Fano 3-folds. I’, Math. USSR. Izv. 11, no. 3 (1977), 485–527.Izv. Akad. Nauk SSSR Ser Mat.41, no. 3 (1977), 516–562).
ISKOVSKIKH, V.A.: ‘Fano 3-folds. I’, Math. USSR. Izv. 11, no. 3 (1977), 485–527.Izv. Akad. Nauk SSSR Ser Mat.41, no. 3 (1977), 516–562). 1
ISKOVSKIKH, V.A.: ‘Fano 3-folds. II’, Math. USSR. Izv. 12, no. 3 (1978), 469–506.
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BUKHSHTAB, A.A.: Number theory, Moscow, 1966 (in Russian).
HALL, R.R.: ‘A note on Farey series’, J. London Math. Soc. 2 (1970), 139–148.
HARDY, G.H. and WRIGHT, E.M.: An introduction to the theory of numbers, Oxford Univ. Press, 1979.
COLLINGWOOD, E.F. and LOHWATER, A.J.: The theory of cluster sets, Cambridge Univ. Press, 1966.
PRIWALOW, I.I. [I.I. Privalov]: Randeigenschaften analytischer Funktionen, Deutsch. Verlag Wissenschaft., 1956 (translated from the Russian).
GOLUZIN, G.M.: Geometric theory of functions of a complex variable, Amer. Math. Soc., 1969 (translated from the Russian).
FATOU, P.: ‘Series trigonométriques et séries de Taylor’, Acta Math. 30 (1906), 335–400.
PRIVALOV, LI. and KUZNETSOV, P.L: ‘On boundary problems and various classes of harmonic and subharmonic functions on an arbitrary domain’, Mat. Sb. 6, no. 3 (1939), 345–376 (in Russian). French summary.
SOLOMENTSEV, E.D.: ‘On boundary values of subharmonic functions’, Czechoslovak. Math. J. 8 (1958), 520–536 (in Russian). French summary.
ZYGMUND, A.: Trigonometric series, 1-2, Cambridge Univ. Press, 1979.
RUDIN, W.: Function theory in poly discs, Benjamin, 1969.
PRIWALOW, I.I. [I.I. Privalov]: Randeigenschaften analytischer Funktionen, Deutsch. Verlag Wissenschaft., 1956 (translated from the Russian).
KHENKIN, G.M. and CHIRKA, E.M.: ‘Boundary properties of holomorphic functions of several complex variables’, J. Soviet Math. 5, no. 5 (1976), 612–687.
Itogi Nauk. i Tekhn. Sovr. Probl. Mat.4 (1975), 13–142)
LANDAU, E.: ‘Darstellung und Begründung einiger neuerer Ergebnisse der Funktionentheorie’, in Das Kontinuum und andere Monographien, Chelsea, reprint, 1973.
HOFFMAN, K.: Banach spaces of analytic functions, Prentice-Hall, 1962.
RUDIN, W.: Function theory in the unit ball of C n, Springer, 1980.
STEIN, E.M.: Boundary behavior of holomorphic functions of several complex variables, Princeton Univ. Press, 1972.
NAGEL, A. and STEIN, E.M.: ‘On certain maximal functions and approach regions’, Adv. in Math. 54 (1984), 83–106.
FATOU, P.: ‘Séries trigonométriques et séries de Taylor’, Acta Math. 30 (1906), 335–400.
SAKS, S.: Theory of the integral, Hafner, 1952 (translated from the Polish).
NATANSON, I.P.: Theorie der Funktionen einer reellen Veränderlichen, H. Deutsch, Frankfurt a.M., 1961 (translated from the Russian).
HEWITT, E. and STROMBERG, K.: Real and abstract analysis, Springer, 1965.
HALMOS, P.R.: Measure theory, v. Nostrand, 1950.
FAVARD, J.: ‘Sur l’approximation des fonctions périodiques par des polynomes trigonometriques’, C.R. Acad. Sci. Paris 203 (1936), 1122–1124.
TIKHOMIROV, V.M.: Some questions in approximation theory, Moscow, 1976 (in Russian).
FAVARD, J.: ‘Une définition de la longueur et de l’aire’, C.R. Acad. Sci. Paris 194 (1932), 344–346.
FEDERER, H.: Geometric measure theory, Springer, 1969.
FAVARD, J.: ‘Sur les meilleurs procédes d’approximation de certain classes’, Bull. Sci. Math. 61 (1937), 209–224.
STECHKIN, S.B.: ‘On best approximation of certain classes of periodic functions by trigonometric functions’, Izv. Akad. Nauk SSSR Ser. Mat. 20, no. 5 (1956), 643–648 (in Russian).
DZYADYK, V.K.: ‘Best approximation on classes of periodic functions defined by kernels which are integrals of absolutely monotone functions’, Izv. Akad. Nauk SSSR Ser. Mat. 23, no. 6 (1959), 933–950 (in Russian).
KORNEĭCHUK, N.P.: Extremal problems of approximation theory, Moscow, 1976 (in Russian).
FEINERMAN, R.P. and NEWMAN, D.J.: Polynomial approximation, Williams & Wilkins, Chapt. IV. 4.
FAVARD, J.: ‘Sur les polynomes de Tchebicheff, C.R. Acad. Sci. Paris 200 (1935), 2052–2053.
SZEGÖ, G.: Orthogonal polynomials, Amer. Math. Soc., 1975.
ARKHANGEL’SKIĭ, A.V. and Ponomarev, V.I.: Fundamentals of general topology: problems and exercises, Reidel, 1984 (translated from the Russian).
ARKHANGEL’skiĭ, A.V.: ‘A class of spaces which contains all metric and all locally compact spaces’, Mat. Sb. 67, no. 1 (1965), 55–88 (in Russian).
FILIPPOV, V.V.: ‘The perfect image of a paracompact feathered space’, Soviet Math. Dokl. 8 (1967), 1151–1153.
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PASYNKOV, B.A.: ‘ALmost-metrizable topological groups’, Soviet Math. Dokl. 7 (1966), 404–408.
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MORITA, K.: ‘Products of normal spaces with metric spaces’, Math. Ann. 154 (1964), 365–382.
NAGATA, J.: Modern general topology, North-Holland, 1985.
GRUENHAGE, G.: ‘Generalized metric spaces’, in K. Kunen and J.E. Vaughan (eds.): Handbook of Set-Theoretic Topology, North-Holland, 1984, pp. 423–501.
GRUENHAGE, G.: ‘Generalized metric spaces’, in K. Kunen and J.E. Vaughan (eds.): Handbook of Set-Theoretic Topology North-Holland, 1984, pp. 423–501.
FEDOROV, E.S.: The symmetry and structure of crystals. Fundamental works, Moscow, 1949, pp. 111–255 (in Russian).
BARY, N.K. [N. K. Bari]: A treatise on trigonometric series, Pergamon, 1964 (translated from the Russian).
FEJÉR, L.: ‘Untersuchungen über Fouriersche Reihen’, Math. Ann. 58 (1903), 51–69.
ACHBEZER, N.I. [N.I. Akhiezer]: Theory of approximation, F. Ungar, 1956 (translated from the Russian).
ZYGMUND, A.: Trigonometric series, 1–2, Cambridge Univ. Press, 1979.
NATANSON, I.P.: Constructive function theory, 1–3, F. Ungar, 1964–1965 (translated from the Russian).
TIKHOMIROV, V.M.: Some questions in approximation theory, Moscow, 1976 (in Russian).
FEJÉR, L.: ‘Untersuchungen uber Fouriersche Reihen’, Math. Ann. 58 (1903), 51–69.
LEBESGUE, H.: ‘Recherches sur la convergence de séries de Fourier’, Math. Ann. 61 (1905), 251–280.
BARY, N.K. [N.K. Bari]: A treatise on trigonometric series, Pergamon, 1964 (translated from the Russian).
ZYGMUND, A.: Trigonometric series, 1–2, Cambridge Univ. Press, 1979.
DYNKIN, E.B.: Markov processes, 1–2, Springer, 1965 (translated from the Russian).
GIRSANOV, I.V.: ‘On transforming a certain class of stochastic processes by absolutely continuous substitution of measures’, Theor. Probab. Appl 5, no. 3 (1960), 285–301.
Teor. Veroyatnost. i Primenen.5, no. 3 (1960), 314–330)
MOLCHANOV, S.A.: ‘Strong Feller property of diffusion processes on smooth manifolds’, Theor. Probab. Appl 13, no. 3 (1968), 471–475.
Teor. Veroyatnost. i Primenen.13, no. 3 (1968), 493–498)
TUOMINEN, P. and TWEEDIE, R.: ‘Markov chains with continuous components’, Proc. London Math. Soc. 38 (1979), 89–114.
FOGUEL, S.: ‘The ergodic theory of positive operators on continuous functions’, Ann. Scuola Norm. Sup. Pisa 27, no. 1 (1973), 19–51.
SINE, R.: ‘Sample path convergence of stable Markov processes II’, Indiana Univ. Math. J. 25, no. 1 (1976), 23–43.
SMIRNOV, S.N.: ‘On the asymptotic behavior of Feller chains’, Soviet Math. Dokl 25, no. 2 (1982), 399–403.
Dokl Akad. Nauk SSSR 263, no. 3 (1982), 554–558)
REVUZ, D.: Markov chains, North-Holland, 1975.
ZHDANOK, A.I.: ‘Ergodic theorems for nonsmooth Markov processes’, in Topological spaces and their mappings, Riga, 1981, pp. 18–33 (in Russian). English summary.
SHUR, M.G.: ‘Invariant measures for Markov chains and Feller extensions of chains’, Theory Probab. Appl. 26, no. 3 (1981), 485–497.
Teor. Veroyatnost. I Primenen. 26, no. 3 (1981), 496–509)
DELLACHERIE, C. and MEYER, P.A.: Probabilities and potentialC, North-Holland, 1988 (translated from the French).
FELLER, W.: An introduction to probability theory and its applications, 2, Wiley, 1966, Chapt. X.
LOÈVE, M.: Probability theory, Princeton Univ. Press, 1963, Chapt. XIV.
CHUNG, K.L.: Lectures from Markov processes to Brownian motion, Springer, 1982.
WENTZELL, A.D.: A course in the theory of stochastic processes, McGraw-Hill, 1981.
ETHIER, S.N. and KURTZ, T.G.: Markov processes, Wiley, 1986.
ALEXANDRIA, Diophantus of: Aritmetika and the book on polygonal numbers, Moscow, 1974 (in Russian; translated from the Greek).
EDWARDS, H.M.: Fermat’s last theorem. A genetic introduction to algebraic number theory, Springer, 1977.
KUMMER, E.: ‘Bestimmung der Anzahl nicht aquivalenter Classen für die aus λten Wurzeln der Einheit gebildeten complexen Zahlen’, J. Reine Angew. Math. 40 (1850), 93–116.
KUMMER, E.: ‘Zwei besondere Untersuchungen über die Classen-Anzahl und über die Einheiten der aus λten Wurzeln der Einheit gebildeten complexen Zahlen’, J. Reine Angew. Math. 40 (1850), 117–129.
KRUMMER, E.: ‘Algemeiner Beweis des Fermat’schen Satzes, dass die Gleichung xλ + yλ = zλ durch ganze Zahlen unlosbar ist, fur diejenige Potenz-Exponenten λ, welche ungerade Primzahlen sind und in den Zahlern der ersten (λ-3)/2 Bernoullischen Zahlen als Faktoren nicht vorkommen’, J. Reine Angew. Math. 40 (1950), 130–138.
BOREVICH, Z.I. and Shafarevich, I.R.: Theorie of numbers, Acad. Press, 1966 (translated from the Russian).
KUMMER, E.: ‘Einige Sätze über die aus den Wurzeln der Gleichung a λ = 1 gebildeten complexen Zahlen, für den Fall, dass die Klassenanzahl durch λ teilbar ist, nebst Anwendung derselben auf einen weiteren Beweis des letzten Fermat’schen Lehrsatzes’, Abk Akad. Wiss. Berlin, Math. Kl. (1857), 41–74.
VANDIVER, H.: ‘Fermat’s last theorem’, Amer. Math. Monthly 53 (1946), 555–578.
RIBENBOIM, P.: 13 lectures on Fermat’s last theorem, Springer, 1979.
KRASNER, M.: ‘Sur le premier cas du theoreme de Fermat’, CK Acad Sci. Paris 199 (1934), 256–258.
BRÜCKNER, H.: ‘Zum Beweis des ersten Falles der Fermatschen Vermutung für pseudo requlären Primzahlen l’, J. ReineAngew. Math. 253 (1972), 15–18.
REMOROV, P.N.: ‘On Kummer’s theorem’, Uchen. Zap. Leningrad. Gosudarstv. Univ. Ser. Mat. Nauk 144, no. 23 (1952), 26–34 (in Russian).
EICHLER, M.: ‘Eine Bemerkung zur Fermatschen Vermutung’, ActaArith. 11 (1965), 129–131.
VANDIVER, H.: ‘Fermat’s last theorem and the second factor in the cyclotomic class number’, Bull. Amer. Math. Soc. 40 (1934), 118–126.
VANDIVER, H.: ‘On Fermat’s last theorem’, Trans. Amer. Math. Soc. 31 (1929), 613–642.
VANDIVER, H.: ‘Examination of methods of attack on the second case of Fermat’s last theorem’, Proc. Nat. Acad. Sci. USA 40 (1954), 732–735.
WAGSTAFF, S.: ‘The irregular primes to 125 000’, Math. Comp. 32 (1978), 583–591.
WIEFERICH, A.: ‘Zum letzter Fermatschen Theorem’, J. Peine Angew. Math. 136 (1909), 293–302.
MIRIMANOFF, D.: ‘Zum letzter Fermatschen Theorem’, J. Reine Angew. Math. 139 (1911), 309–324.
LEHMER, D.H.: ‘On Fermat’s quotient, base 2’, Math. Comp. 36 (1981), 289–290.
FURTWÄNGLER, P.: ‘Letzter Fermat’scher Satz und Eisenstein’sches Reziprozitätsprinzip’, Sitzungsber. Akad Wiss. Wien Math-Naturwiss. Kl. IIa 121 (1912), 589–592.
TERJANIAN, G.: ‘Sur l’equation x29 + y2p = z2p’, C.R. Acad. Sci. Paris A285-B285, no. 16 (1977), 973A–975A. English abstract.
INKERI, K.: ‘Abschätzungen für eventuelle Lösungen der Gleichung im Fermatschen problem’, Ann. Univ. Turku Ser. A 16, no. 1 (1953), 3–9.
POSTNIKOV, M.M.: An introduction to algebraic number theory, Moscow, 1982 (in Russian).
FALTINGS, G.: ‘Endichkeitssätze für abelsche Varietäten über Zahlkörpern’, Invent. Math. 73 (1983), 349–366.
HEATH-BROWN, D.R.: ‘Fermat’s last theorem for “almost all” exponents’, Bull London Math. Soc. 17 (1985), 15–16.
ADLEMAN, L.M. and HEATH-BROWN, D.R.: ‘The first case of Fermat’s last theorem’, Invent. Math. 79 (1985), 409–416.
WAGON, S.: ‘Fermat’s last theorem’, Math. Intelligencers, no. 1 (1986), 59–61.
RIBENBOIM, P.: ‘Recent results about Fermat’s last theorem’, Cand. Math. Bull. 20 (1977), 229–242.
VINOGRADOV, I.M.: Elements of number theory, Dover, reprint, 1954 (translated from the Russian).
HARDY, G.H. and WRIGHT, E.M.: Introduction to the theory of numbers, Oxford Univ. Press, 1979.
SAVELOV, A.A.: Plane curves, Moscow, 1960 (in Russian).
LAWRENCE, J.D.: A catalog of special plane curves, Dover, reprint, 1972.
FERMI, E.: ‘Sopra i fenomeni che awengono in vinicinanza di una linea ovaria’, Atti R Accad. Lincei Rend’, CI. Sci. Fis. Mat. Nat. 31 (1922), 21–51.
RASHEWSKI, P.K. [P.K. Rashevskiĭ]: Riemannsche Geometrie und Tensoranalyse, Deutsch. Verlag Wissenschaft., 1959 (translated from the Russian).
KUROSH, A.G.: Higher algebra, Mir, 1972 (translated from the Russian).
FEYNMAN, R.P.: ‘Space-time approach to non-relativistic quantum mechanics’, Rev. Modern Phys. 20 (1948), 367–387.
KAC, M.: ‘On some connections between probability theory and differential and integral equations’, in Proc. 2nd Berkeley symp. math, statist, probab., Univ. California Press, 1951, pp. 189–215.
GINIBRE, J.: ‘Some applications of functional integration in statistical mechanics’, in C. DeWitt and R. Stora (eds.): Statistical mechanics and quantum field theory, Gordon & Breach, pp. 327–427.
SIMON, B.: The P(φ) 2 -Euclidean (quantum) field theory, Princeton Univ. Press, 1974.
DALETSKIĭ, Yu.L.: ‘Integration in function spaces’, Progress in Mathematics 4 (1969), 87–132.
Itogi Nauk. Mat. Anal. 1966 (1967), 83–124)
ALBEVERIO, S. and HOEGH-KROHN, R.: Mathematical theory of Feynman path integrals, Springer, 1976.
GIKHMAN, I.I. and SKOROKHOD, A.V.: The theory of stochastic processes, 3, Springer, 1979 (translated from the Russian).
GOLUBEVA, V.A.: ‘Some problems in the analytic theory of Feynman integrals’, Russian Math. Surveys 31, no. 2 (1976), 135–202.
Uspekhi Mat. Nauk 31, no. 2 (1976), 135–202)
FEYNMAN, R.P. and HIBBS, A.R.: Quantum mechanics and path integrals, McGraw-Hill, 1965.
SCHULMAN, L.S.: Techniques and applications of path integration, Wiley, 1981.
POPOV, V.N.: Functional integrals in quantum field theory, Reidel, 1983 (translated from the Russian).
ANTOINE, J.-P. and TIRAPEGUI, E. (eds.): Functional integration, Plenum, 1980.
SIMON, B.: Functional integration and quantum physics, Acad. Press, 1979.
FEYNMAN, R.P.: ‘Space-time approach to non-relativistic quantum mechanics’, Rev. Modern Phys. 20 (1948), 367–387.
DALETSKII, Yu.L.: ‘Integration in function spaces’, Progress in Mathematics 4 (1969), 87–132.
Itogi Nauk. Mat. Anal. 1966 (1967), 83–124)
ALBEVERIO, S. and HØegh-Krohn, R.: Mathematical theory of Feynman path integrals, Springer, 1976.
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Hazewinkel, M. (1989). F. In: Hazewinkel, M. (eds) Encyclopaedia of Mathematics. Encyclopaedia of Mathematics, vol 3. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-5994-1_3
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