Bibliography for the Complex Exponential Function

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  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. An arithmetic criterion for the values of the exponential function.
    Roy, Damien
    Acta Arith. 97 (2001), no. 2, 183--194, MathSciNet.  
  5. 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.   
  6. Newton's method on the complex exponential function.
    Haruta, Mako E.
    Trans. Amer. Math. Soc. 351 (1999), no. 6, 2499--2513, MathSciNet.  
  7. 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.  
  8. 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.  
  9. 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.  
  10. 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.
  11. 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.   
  12. 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.  
  13. 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.  
  14. 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.
  15. 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.
  16. 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.  
  17. 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.
  18. 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.  
  19. 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.  
  20. Iterating exponential functions with cyclic exponents.
    Baker, I. N.; Rippon, P. J.
    Math. Proc. Cambridge Philos. Soc. 105 (1989), no. 2, 357--375, MathSciNet.  
  21. 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.
  22. 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.  
  23. 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.
  24. Structural Instability of exp(z)  
    Robert L. Devaney  
    Proceedings of the American Mathematical Society, Vol. 94, No. 3. (Jul., 1985), pp. 545-548, Jstor.  
  25. Evaluating ex Using Limits (in Computer Corner)  
    Sheldon P. Gordon  
    The College Mathematics Journal, Vol. 15, No. 1. (Jan., 1984), pp. 63-65.
  26. 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.  
  27. On the Fresnel Integrals (in Notes)  
    Harley Flanders  
    The American Mathematical Monthly, Vol. 89, No. 4. (Apr., 1982), pp. 264-266, Jstor.  
  28. On a Hyperanalytic Geometry for Complex Functions  
    Malcolm Murrill  
    The American Mathematical Monthly, Vol. 87, No. 1. (Jan., 1980), pp. 8-25, Jstor.  
  29. 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.
  30. 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.  
  31. Bounds on the Negative Exponential Function (in Mathematical Notes)  
    Khursheed Alam  
    The American Mathematical Monthly, Vol. 87, No. 4. (Apr., 1980), pp. 290-292.
  32. Excesses of systems of exponential functions. (Russian)
    Sedleckii, A. M.
    Izv. Akad. Nauk SSSR Ser. Mat. 44 (1980), no. 1, 203--218, 240, MathSciNet.  
  33. 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.
  34. Restricted Pade Approximations to the Exponential Function  
    Syvert P. Norsett  
    SIAM Journal on Numerical Analysis, Vol. 15, No. 5. (Oct., 1978), pp. 1008-1029.
  35. 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.
  36. 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.  
  37. On the Exponential Function (in Classroom Notes)  
    Z. A. Melzak  
    The American Mathematical Monthly, Vol. 82, No. 8. (Oct., 1975), pp. 842-844.
  38. 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.
  39. 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.
  40. 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.
  41. On a functional equation for the exponential function of a complex variable.
    Haruki, Hiroshi
    Glasgow Math. J. 12 (1971), 31--34, MathSciNet.  
  42. The Maclaurin Series for ex (in Classroom Notes)  
    J. R. Isbell  
    The American Mathematical Monthly, Vol. 71, No. 9. (Nov., 1964), pp. 1033-1034.
  43. 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.
  44. Applications of the Complex Exponential Integral  
    Murlan S. Corrington  
    Mathematics of Computation, Vol. 15, No. 73. (Jan., 1961), pp. 1-6, Jstor.  
  45. On Generalizations of the Exponential Function  
    S. Tauber  
    The American Mathematical Monthly, Vol. 67, No. 8. (Oct., 1960), pp. 763-767.
  46. 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.
  47. Insertion of ± Signs in e^x  
    Donald J. Newman  
    Proceedings of the American Mathematical Society, Vol. 11, No. 3. (Jun., 1960), pp. 444-446.
  48. 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.
  49. The Exponential Function  
    John G. Kemeny  
    The American Mathematical Monthly, Vol. 64, No. 3. (Mar., 1957), pp. 158-160.
  50. 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.  
  51. 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.  
  52. An arithmetical property of the exponential function.
    Rado, R.
    J. London Math. Soc. 23, (1948). 267--271, MathSciNet.  
  53. 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.
  54. 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.
  55. 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.
  56. 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.
  57. History of the Exponential and Logarithmic Concepts  
    Florian Cajori  
    The American Mathematical Monthly, Vol. 20, No. 7. (Sep., 1913), pp. 205-210, Jstor.  
  58. History of the Exponential and Logarithmic Concepts  
    Florian Cajori  
    The American Mathematical Monthly, Vol. 20, No. 4. (Apr., 1913), pp. 107-117, Jstor.  
  59. History of the Exponential and Logarithmic Concepts  
    Florian Cajori  
    The American Mathematical Monthly, Vol. 20, No. 6. (Jun., 1913), pp. 173-182, Jstor.  
  60. History of the Exponenetial and Logarithmic Concepts  
    Florian Cajori  
    The American Mathematical Monthly, Vol. 20, No. 5. (May, 1913), pp. 148-151, Jstor.  
  61. History of the Exponential and Logarithmic Concepts  
    Florian Cajori  
    The American Mathematical Monthly, Vol. 20, No. 4. (Apr., 1913), pp. 107-117, Jstor.  
  62. History of the Exponential and Logarithmic Concepts  
    Florian Cajori  
    The American Mathematical Monthly, Vol. 20, No. 3. (Mar., 1913), pp. 75-84, Jstor.  
  63. History of the Exponential and Logarithmic Concepts  
    Florian Cajori  
    The American Mathematical Monthly, Vol. 20, No. 2. (Feb., 1913), pp. 35-47, Jstor.  
  64. History of the Exponential and Logarithmic Concepts  
    Florian Cajori  
    The American Mathematical Monthly, Vol. 20, No. 1. (Jan., 1913), pp. 5-14, Jstor.  
  65. 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.

 

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