Bibliography for the Complex Exponential Function

unabridged

 

  1. MC Escher: More Mathematics Than Meets the Eye  
    Sara Robinson
    SIAM News, Vol. 35, No. 8, October 2002
  2. A Generalized Logarithm for Exponential-Linear Equations
    Dan Kalman
    College Math Journal, VOL. 32, NO. 1, January 2001, Jstor.  
  3. Conformality, the exponential function, and world map projections  
    Feeman, Timothy G.
    College Math. J. 32 (2001), no. 5, 334--342, Jstor.  
  4. Rational Approximation to the Exponential Function with Complex Conjugate Interpolation Points
    Wielonsky F.
    Journal of Approximation Theory, August 2001, vol. 111, no. 2, pp. 344-368(25), Ingenta.  
  5. An arithmetic criterion for the values of the exponential function.
    Roy, Damien
    Acta Arith. 97 (2001), no. 2, 183--194, MathSciNet.  
  6. Growth in complex exponential dynamics
    Romera M.; Pastor G.; Alvarez G.; Montoya F.
    Computers and Graphics, February 2000, vol. 24, no. 1, pp. 115-131(17), Ingenta.   
  7. Newton's method on the complex exponential function.
    Haruta, Mako E.
    Trans. Amer. Math. Soc. 351 (1999), no. 6, 2499--2513, MathSciNet.  
  8. The Dynamics of  lambda  z + exp(z)
    Petek P.; Kirchgraber M.U.S.
    Journal of Mathematical Analysis and Applications, June 1998, vol. 222, no. 1, pp. 38-63(26), Ingenta.  
  9. Dynamics of exponential functions.
    Yang, Degui; Hao, Zhifeng; Hua, Xinhou
    Nanjing Daxue Xuebao Shuxue Bannian Kan 15 (1998), no. 2, 168--173, MathSciNet.  
  10. Nondefinability Results for Expansions of the Field of Real Numbers by the Exponential Function and by the Restricted Sine Function  
    Ricardo Bianconi
    The Journal of Symbolic Logic, Vol. 62, No. 4. (Dec., 1997), pp. 1173-1178, Jstor.  
  11. The Stability of the Exponential Equation  
    Roman Ger; Peter Semrl  
    Proceedings of the American Mathematical Society, Vol. 124, No. 3. (Mar., 1996), pp. 779-787, Jstor.  
  12. Model Completeness Results for Expansions of the Ordered Field of Real Numbers by Restricted Pfaffian Functions and the Exponential Function  
    A. J. Wilkie  
    Journal of the American Mathematical Society, Vol. 9, No. 4. (Oct., 1996), pp. 1051-1094.
  13. On the domain of attraction of exp(-exp(-x))
    Geluk J.L.
    Statistics and Probability Letters, 16 December 1996, vol. 31, no. 2, pp. 91-95(5), Ingenta.   
  14. On the Surjectivity of the Exponential Function of Complex Algebraic, Complex Semisimple, and Complex Splittable Lie Groups
    Wustner M.
    Journal of Algebra, September 1996, vol. 184, no. 3, pp. 1082-1092(11), Ingenta.   
  15. Grands degrés de transcendance pour la fonction exponentielle; modification des hypothèses techniques dans la méthode de Brownawell. (French) [Large transcendence degrees for the exponential function; modification of the technical hypotheses in the method of Brownawell]
    Delaunay, Sandra
    Ann. Fac. Sci. Toulouse Math. (6) 5 (1996), no. 1, 69--104, MathSciNet.  
  16. A New Look at an Old Function, exp(i theta)  
    J. G. Simmonds  
    The College Mathematics Journal, Vol. 26, No. 1. (Jan., 1995), pp. 6-10, Jstor.  
  17. A New Functional Equation of Pexider Type Related to the Complex Exponential Function  
    Hiroshi Haruki; Themistocles M. Rassias  
    Transactions of the American Mathematical Society, Vol. 347, No. 8. (Aug., 1995), pp. 3111-3119, Jstor.  
  18. The Matrix Exponential Function and Systems of Differential Equations Using Derive (in Computer Corner)  
    Robert J. Hill; Mark S. Mazur  
    The College Mathematics Journal, Vol. 26, No. 2. (Mar., 1995), pp. 146-151.
  19. Accumulated moment method for estimating parameters of the complex exponential signal models in noise
    Sircar P.; Mukhopadhyay S.
    Signal Processing, August 1995, vol. 45, no. 2, pp. 231-243(13), Ingenta.   
  20. The space of exponential functions associated with a class of differential operator and application.
    Minh, Nguyen Si; Van, Tran Duc; Tuan, Nguyen Si Anh
    Analysis and mechanics of continuous media (Ho Chi Minh City, 1995), 268--281, Publ. HoChiMinh City Math. Soc., 3, HoChiMinh City Math. Soc., Ho Chi Minh City, 1995, MathSciNet.  
  21. Structural stability of exponential functions described by orbit of zero.
    Qiu, Wei Yuan; Yin, Yong Cheng
    Complex Variables Theory Appl. 27 (1995), no. 4, 299--307, MathSciNet.  
  22. On the zeros of the q-analogue exponential function.
    Nelson, Charles A.; Gartley, Michael G.
    J. Phys. A 27 (1994), no. 11, 3857--3881, MathSciNet.
  23. q-exponential functions and gamma functions.
    McAnally, D. S.
    Confronting the infinite (Adelaide, 1994), 246--253, World Sci. Publishing, River Edge, NJ, 1995, MathSciNet.  
  24. Atomic exponential functions. (Russian)
    Gorshkov, A. S.; Kravchenko, V. F.; Rvachëv, V. L.
    Dokl. Akad. Nauk 336 (1994), no. 3, 309--311; translation in Phys. Dokl. 39 (1994), no. 5, 297--299, MathSciNet.  
  25. The exponential function and linearization of quadratic polynomials.
    Erkama, Timo
    Analysis, algebra, and computers in mathematical research (Lulea, 1992), 71--80, Lecture Notes in Pure and Appl. Math., 156, Dekker, New York, 1994, MathSciNet.  
  26. Structurally unstable exponential functions. (Chinese)
    Qiu, Wei Yuan
    Chinese J. Contemp. Math. 15 (1994), no. 2, 155--164, MathSciNet.  
  27. Structurally unstable exponential functions. (Chinese)
    Qiu, Wei Yuan
    Chinese Ann. Math. Ser. A 15 (1994), no. 2, 164--170, MathSciNet.  
  28. On optimal including circular approximation for the range of a complex exponential function.
    Petkovi'c, Lj. D.
    Z. Angew. Math. Mech. 73 (1993), no. 2, 109--116, MathSciNet.  
  29. An Approximation Connected with the Exponential Function  
    K. Soni; R. P. Soni  
    Proceedings of the American Mathematical Society, Vol. 114, No. 4. (Apr., 1992), pp.  909-918.
  30. Recurrence relations in exponential functions and in damped sinusoids and their applications in electronics.
    Lahr, Joseph
    Applications of Fibonacci numbers, Vol. 4 (Winston-Salem, NC, 1990), 189--202, Kluwer Acad. Publ., Dordrecht, 1991, MathSciNet.  
  31. The Exponential of Iteration of e^x - 1  
    Peter L. Walker  
    Proceedings of the American Mathematical Society, Vol. 110, No. 3. (Nov., 1990), pp. 611-620, Jstor.  
  32. Kato-Protter type inequalities, bounded vectors and the exponential function.
    Szafraniec, F. H.
    Ann. Polon. Math. 51 (1990), 303--312, MathSciNet.  
  33. Degrees of transcendence of some fields that are generated by values of an exponential function. (Russian)
    Nesterenko, Yu. V.
    Mat. Zametki 46 (1989), no. 3, 40--49, 127; translation in Math. Notes 46 (1989), no. 3-4, 706--712 (1990), MathSciNet.  
  34. Iterating exponential functions with cyclic exponents.
    Baker, I. N.; Rippon, P. J.
    Math. Proc. Cambridge Philos. Soc. 105 (1989), no. 2, 357--375, MathSciNet.  
  35. On the Zeros of the Taylor Polynomials Associated with the Exponential Function  
    Brian Conrey; Amit Ghosh  
    The American Mathematical Monthly, Vol. 95, No. 6. (Jun. - Jul., 1988), pp. 528-533.
  36. The Differentiability of the Hairs of exp(Z)  
    M. Viana da Silva  
    Proceedings of the American Mathematical Society, Vol. 103, No. 4. (Aug., 1988), pp. 1179-1184, Jstor.  
  37. On the zeros of the Taylor polynomials associated with Douady, Adrien; Goldberg, Lisa R. The nonconjugacy of certain exponential functions.
    Conrey, Brian; Ghosh, Amit
    Holomorphic functions and moduli, Vol. I (Berkeley, CA, 1986), 1--7, Math. Sci. Res. Inst. Publ., 10, Springer, New York, 1988, MathSciNet.  
  38. Counterexample to the Spectral Mapping Theorem for the Exponential Function  
    J. Hejtmanek; Hans G. Kaper  
    Proceedings of the American Mathematical Society, Vol. 96, No. 4. (Apr., 1986), pp. 563-568.
  39. Structural Instability of exp(z)  
    Robert L. Devaney  
    Proceedings of the American Mathematical Society, Vol. 94, No. 3. (Jul., 1985), pp. 545-548, Jstor.  
  40. Rational approximations to the exponential function with two complex conjugate interpolation points.
    Hairer, Ernst; Iserles, Arieh; Nørsett, Syvert P.
    SIAM J. Math. Anal. 16 (1985), no. 4, 814--821, MathSciNet.  
  41. Evaluating ex Using Limits (in Computer Corner)  
    Sheldon P. Gordon  
    The College Mathematics Journal, Vol. 15, No. 1. (Jan., 1984), pp. 63-65.
  42. Accurate Computation of Divided Differences of the Exponential Function  
    A. McCurdy; K. C. Ng; B. N. Parlett  
    Mathematics of Computation, Vol. 43, No. 168. (Oct., 1984), pp. 501-528, Jstor.  
  43. Some applications of Nevanlinna theory to mathematical logic: identities of exponential functions.
    Henson, C. Ward; Rubel, Lee A.
    Trans. Amer. Math. Soc. 282 (1984), no. 1, 1--32, MathSciNet.  
  44. A modified proof of transcendence of the p-adic exponential function.
    Laohakosol, Vichian
    Southeast Asian Bull. Math. 8 (1984), no. 1, 5--9, MathSciNet.  
  45. Iteration of exponential functions.
    Baker, I. N.; Rippon, P. J.
    Ann. Acad. Sci. Fenn. Ser. A I Math. 9 (1984), 49--77, MathSciNet.  
  46. On the Fresnel Integrals (in Notes)  
    Harley Flanders  
    The American Mathematical Monthly, Vol. 89, No. 4. (Apr., 1982), pp. 264-266, Jstor.  
  47. The exponential function characterized by an approximate functional equation.
    Elliott, P. D. T. A.
    Illinois J. Math. 26 (1982), no. 3, 503--518, MathSciNet.  
  48. Indépendance algébrique de valeurs de fonctions exponentielles p-adiques. (French) [Algebraic independence of values of p-adic exponential functions]
    Philippon, P.
    J. Reine Angew. Math. 329 (1981), 42--51, MathSciNet.  
  49. Convergence of rational approximations to a set of exponential functions. (Russian)
    Aptekarev, A. I.
    Vestnik Moskov. Univ. Ser. I Mat. Mekh. 1981, no. 1, 68--74, 108, MathSciNet.  
  50. On a Hyperanalytic Geometry for Complex Functions  
    Malcolm Murrill  
    The American Mathematical Monthly, Vol. 87, No. 1. (Jan., 1980), pp. 8-25, Jstor.  
  51. Subseries of the Power Series for e^x  
    Lee Rubel; Kenneth Stolarsky  
    The American Mathematical Monthly, Vol. 87, No. 5. (May, 1980), pp. 371-376.
  52. Zeros of Successive Derivatives of Entire Functions of the Form h(z)exp(-ez)  
    Albert Edrei  
    Transactions of the American Mathematical Society, Vol. 259, No. 1. (May, 1980), pp. 207-226, Jstor.  
  53. Bounds on the Negative Exponential Function (in Mathematical Notes)  
    Khursheed Alam  
    The American Mathematical Monthly, Vol. 87, No. 4. (Apr., 1980), pp. 290-292.
  54. Excesses of systems of exponential functions. (Russian)
    Sedleckii, A. M.
    Izv. Akad. Nauk SSSR Ser. Mat. 44 (1980), no. 1, 203--218, 240, MathSciNet.  
  55. On the Generalized Pade Approximations to the Exponential Function  
    Arieh Iserles  
    SIAM Journal on Numerical Analysis, Vol. 16, No. 4. (Aug., 1979), pp. 631-636.
  56. Restricted Pade Approximations to the Exponential Function  
    Syvert P. Norsett  
    SIAM Journal on Numerical Analysis, Vol. 15, No. 5. (Oct., 1978), pp. 1008-1029.
  57. Simultaneous approximation of numbers connected with the exponential function.
    Waldschmidt, Michel
    J. Austral. Math. Soc. Ser. A 25 (1978), no. 4, 466--478, MathSciNet.  
  58. On the density of the image of the exponential function.
    Hofmann, Karl H.; Mukherjea, Arunava
    Math. Ann. 234 (1978), no. 3, 263--273, MathSciNet.  
  59. Numbers Generated by the Reciprocal of  e^x - x - 1  
    F. T. Howard  
    Mathematics of Computation, Vol. 31, No. 138. (Apr., 1977), pp. 581-598.
  60. On a characteristic property of the exponential function.
    Kobayashi, Tadashi
    Kodai Math. Sem. Rep. 29 (1977), no. 1-2, 130--156, MathSciNet.  
  61. Excesses of systems of exponential functions. (Russian)
    Sedleckii, A. M.
    Mat. Zametki 22 (1977), no. 6, 803--814, MathSciNet.  
  62. On the arithmetic properties of certain values of the exponential function.
    Väänänen, K.
    Studia Sci. Math. Hungar. 11 (1976), no. 3-4, 399--405, MathSciNet.  
  63. On the Exponential Function (in Classroom Notes)  
    Z. A. Melzak  
    The American Mathematical Monthly, Vol. 82, No. 8. (Oct., 1975), pp. 842-844.
  64. Some inequalities connected with exponential function.
    Marti'c, Branislav
    Mat. Vesnik 12(27) (1975), no. 2, 163--165, MathSciNet.  
  65. Expansions in exponential functions. (Russian)
    Sedleckii, A. M.
    Sibirsk. Mat. Z. 16 (1975), no. 4, 820--829, 886, MathSciNet.  
  66. A New Characterization of the Exponential Function (in Mathematical Notes)  
    G. P. Kapoor  
    The American Mathematical Monthly, Vol. 81, No. 4. (Apr., 1974), pp. 380-381.
  67. The algebraic independence of certain numbers related by the exponential function.
    Brownawell, W. Dale
    J. Number Theory 6 (1974), 22--31, MathSciNet.  
  68. Algebraic independence of several values of the exponential function. (Russian)
    Cudnovskii, G. V.
    Mat. Zametki 15 (1974), 661--672, MathSciNet.  
  69. The stability of the completeness and of the minimality in L2 of a system of exponential functions. (Russian)
    Sedleckii, A. M.
    Mat. Zametki 15 (1974), 213--219, MathSciNet.  
  70. The arithmetic properties of the values of the exponential function at nonalgebraic points. (Russian)
    Smelev, A. A.
    Izv. Vys s. Ucebn. Zaved. Matematika 1973, no. 10(137), 90--99, MathSciNet.  
  71. On R. Von Mises' Condition for the Domain of Attraction of exp(-e -x )1 (in Short Communications)  
    A. A. Balkema; L. De Haan  
    The Annals of Mathematical Statistics, Vol. 43, No. 4. (Aug., 1972), pp. 1352-1354.
  72. The algebraic independence of certain values of the exponential function.
    Brownawell, Dale
    Norske Vid. Selsk. Skr. (Trondheim) 1972, no. 23, 5 pp., MathSciNet.  
  73. Some transcendence results for the exponential function.
    Brownawell, W. Dale
    Norske Vid. Selsk. Skr. (Trondheim) 1972, no. 11, 2 pp., MathSciNet.  
  74. Continuation periodic in the mean and bases of exponential functions in Lp. (Russian)
    Sedleckii, A. M.
    Mat. Zametki 12 (1972), 37--42, MathSciNet.  
  75. The properties of sequences of linear combinations of functions close to exponential functions. (Russian)
    Kasimov, È. I.
    Akad. Nauk Azerbai dzan. SSR Dokl. 28 (1972), no. 2, 9--13, MathSciNet.  
  76. The Diophantine approximations of values of an exponential function and the solutions of certain transcendental equations. (Russian)
    Galockin, A. I.
    Vestnik Moskov. Univ. Ser. I Mat. Meh. 27 (1972), no. 3, 16--23, MathSciNet.  
  77. The Convergence of Rational Functions of Best Approximation to the Exponential Function  
    E. B. Saff  
    Transactions of the American Mathematical Society, Vol. 153. (Jan., 1971), pp. 483-493.
  78. On a functional equation for the exponential function of a complex variable.
    Haruki, Hiroshi
    Glasgow Math. J. 12 (1971), 31--34, MathSciNet.  
  79. Bases of exponential functions in L2. (Russian)
    Kacnel'son, V. È.
    Funkcional. Anal. i Prilo\v zen. 5 1971 no. 1, 37--47, MathSciNet.  
  80. The Maclaurin Series for ex (in Classroom Notes)  
    J. R. Isbell  
    The American Mathematical Monthly, Vol. 71, No. 9. (Nov., 1964), pp. 1033-1034.
  81. The Existence and Uniqueness of the Exponential Function as the Solution of  f' = f,  f(0) =1  (in Classroom Notes)  
    Richard L. Bishop  
    The American Mathematical Monthly, Vol. 70, No. 3. (Mar., 1963), pp. 316-319.
  82. On the Riesz basis of exponential functions. (Russian)
    Golovin, V. D.
    Dokl. Akad. Nauk SSSR 145 1962 27--30, MathSciNet.  
  83. A Diophantine equation with a matrix exponential function. (Russian)
    Muhutdinov, R. H.
    Dokl. Akad. Nauk SSSR 142 1962 36--37, MathSciNet.  
  84. Applications of the Complex Exponential Integral  
    Murlan S. Corrington  
    Mathematics of Computation, Vol. 15, No. 73. (Jan., 1961), pp. 1-6, Jstor.  
  85. On Generalizations of the Exponential Function  
    S. Tauber  
    The American Mathematical Monthly, Vol. 67, No. 8. (Oct., 1960), pp. 763-767.
  86. The Toeplitz-Silverman Theorem and the Definition of ex (in Classroom Notes)  
    M. I. Aissen  
    The American Mathematical Monthly, Vol. 67, No. 1. (Jan., 1960), pp. 70-71.
  87. Insertion of ± Signs in e^x  
    Donald J. Newman  
    Proceedings of the American Mathematical Society, Vol. 11, No. 3. (Jun., 1960), pp. 444-446.
  88. A Characterization of the Exponential Function (in Mathematical Notes)  
    S. G. Ghurye  
    The American Mathematical Monthly, Vol. 64, No. 4. (Apr., 1957), pp. 255-257.
  89. The Exponential Function  
    John G. Kemeny  
    The American Mathematical Monthly, Vol. 64, No. 3. (Mar., 1957), pp. 158-160.
  90. On the Solution of  f(f(z)) = e^z - 1  and its Domain of Regularity  
    Robert Osserman  
    Proceedings of the American Mathematical Society, Vol. 8, No. 2. (Apr., 1957), pp. 262-263, Jstor.  
  91. The Zeros of the Partial Sums of e^z
    K. E. Iverson  
    Mathematical Tables and Other Aids to Computation, Vol. 7, No. 43. (Jul., 1953), pp. 165-168, Jstor.  
  92. An arithmetical property of the exponential function.
    Rado, R.
    J. London Math. Soc. 23, (1948). 267--271, MathSciNet.  
  93. Numbers Generated by the Function e^(e^x-1)  
    G. T. Williams  
    The American Mathematical Monthly, Vol. 52, No. 6. (Jun. - Jul., 1945), pp. 323-327.
  94. Fitting the Exponential Function and the Gompertz Function by the Method of Least Squares  
    Paul Matthew Stoner  
    Journal of the American Statistical Association, Vol. 36, No. 216. (Dec., 1941), pp. 515-518.
  95. On Some Series Arising From a Definition of the Exponential Function  
    J. K. L. MacDonald; F. R. Sharpe  
    The American Mathematical Monthly, Vol. 44, No. 5. (May, 1937), pp. 312-315.
  96. Discussions: Relating to the Exponential Function (in Questions and Discussions)  
    Otto Dunkel  
    The American Mathematical Monthly, Vol. 24, No. 5. (May, 1917), pp. 244-246.
  97. History of the Exponential and Logarithmic Concepts  
    Florian Cajori  
    The American Mathematical Monthly, Vol. 20, No. 7. (Sep., 1913), pp. 205-210, Jstor.  
  98. History of the Exponential and Logarithmic Concepts  
    Florian Cajori  
    The American Mathematical Monthly, Vol. 20, No. 4. (Apr., 1913), pp. 107-117, Jstor.  
  99. History of the Exponential and Logarithmic Concepts  
    Florian Cajori  
    The American Mathematical Monthly, Vol. 20, No. 6. (Jun., 1913), pp. 173-182, Jstor.  
  100. History of the Exponenetial and Logarithmic Concepts  
    Florian Cajori  
    The American Mathematical Monthly, Vol. 20, No. 5. (May, 1913), pp. 148-151, Jstor.  
  101. History of the Exponential and Logarithmic Concepts  
    Florian Cajori  
    The American Mathematical Monthly, Vol. 20, No. 4. (Apr., 1913), pp. 107-117, Jstor.  
  102. History of the Exponential and Logarithmic Concepts  
    Florian Cajori  
    The American Mathematical Monthly, Vol. 20, No. 3. (Mar., 1913), pp. 75-84, Jstor.  
  103. History of the Exponential and Logarithmic Concepts  
    Florian Cajori  
    The American Mathematical Monthly, Vol. 20, No. 2. (Feb., 1913), pp. 35-47, Jstor.  
  104. History of the Exponential and Logarithmic Concepts  
    Florian Cajori  
    The American Mathematical Monthly, Vol. 20, No. 1. (Jan., 1913), pp. 5-14, Jstor.  
  105. On Independent Definitions of the Functions Log(x) and e^x  
    Emory McClintock  
    American Journal of Mathematics, Vol. 14, No. 1. (Oct., 1891), pp. 72-86.

 

 Return to the Complex Analysis Project

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2003