Bibliography for Power Series

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  1. An algorithmic approach to exact power series solutions of second order linear homogeneous differential equations with polynomial coefficients
    Kiymaz O.; Mirasyedioglu S.
    Applied Mathematics and Computation, 1 July 2003, vol. 139, no. 1, pp. 165-178(14), Ingenta.  
  2. Blossoming: from Polynomials to Power Series
    Mazure M-L.
    Numerical Algorithms, June 2002, vol. 30, no. 2, pp. 141-155(15), Ingenta.  
  3. Fast Summation of Power Series with Coefficients Analytic at Infinity
    Sommariva A.; Vianello M.; Zanovello R.
    Numerical Algorithms, May 2001, vol. 27, no. 1, pp. 77-87(11), Ingenta.  
  4. On the power series expansions for the sine and cosine
    Stroethoff K.
    International Journal of Mathematical Education in Science and Technology, 1 September 2001, vol. 32, no. 5, pp. 793-794(2), Ingenta.  
  5. The Nevanlinna characteristics and maximum modulus of gap power series. Dedicated to A. A. Golc'dberg on the occasion of his 70th anniversary.
    Skaskiv, O. B.; Chyzhykov, I. E.
    Mat. Stud. 13 (2000), no. 2, 125--133, MathSciNet.  
  6. Summation of power series in particle physics
    Fischer J.
    Reports on Mathematical Physics, February 1999, vol. 43, no. 1, pp. 109-122(14), Ingenta.  
  7. On certain generalised power series.
    Constantinescu, Gruia
    An. Univ. Bucuresti Mat. 47 (1998), no. 1, 25--32, MathSciNet.  
  8. Reversion of Power Series and the Extended Raney Coefficients  
    Charles Ching-an Cheng; James H. McKay; Jacob Towber; Stuart Sui-Sheng Wang; David L. Wright  
    Transactions of the American Mathematical Society, Vol. 349, No. 5. (May, 1997), pp. 1769-1782, Jstor.  
  9. An efficient FFT-based algorithm for power series expansions
    Chyi H.; Shih Y.-P.; Wu R.-Y.
    Computers and Chemical Engineering, 1997, vol. 21, no. 9, pp. 1043-1049(7), Ingenta.   
  10. Similarities Between Fourier and Power Series  
    Richard Askey; Deborah Tepper Haimo  
    American Mathematical Monthly, Vol. 103, No. 4. (Apr., 1996), pp. 297-304, Jstor.  
  11. Overconvergent Power Series and Conformal Maps
    Gehlen W.
    Journal of Mathematical Analysis and Applications, March 1996, vol. 198, no. 2, pp. 490-505(16), Ingenta.  
  12. A generalization of power series to real several dimensions.
    Wada, Masaaki
    Analysis of discrete groups (Kyoto, 1995). Surikaisekikenkyusho Kokyuroku No. 967 (1996), 196--210, MathSciNet.  
  13. Complex Power Series-A Vector Field Visualization (in Notes)  
    Alan D. Gluchoff  
    Mathematics Magazine, Vol. 66, No. 3. (Jun., 1993), pp. 189-191, Jstor.  
  14. Multisummability of formal power series solutions of nonlinear meromorphic differential equations.
    Braaksma, Boele L. J.
    Ann. Inst. Fourier (Grenoble) 42 (1992), no. 3, 517--540, MathSciNet.  
  15. The Radius of Convergence of Power Series Solutions to Linear Differential Equations (in The Teaching of Mathematics)  
    Isom H. Herron  
    American Mathematical Monthly, Vol. 96, No. 9. (Nov., 1989), pp. 824-827, Jstor.  
  16. Differentiation of Power Series (in The Teaching of Mathematics)  
    R. Vyborny  
    American Mathematical Monthly, Vol. 94, No. 4. (Apr., 1987), pp. 369-370, Jstor.  
  17. Best Rational Approximations of Entire Functions Whose Maclaurin Series Coefficients Decrease Rapidly and Smoothly  
    A. L. Levin; D. S. Lubinsky  
    Transactions of the American Mathematical Society, Vol. 293, No. 2. (Feb., 1986), pp.  533-545, Jstor.  
  18. An Acceleration Method for the Power Series of Entire Functions of Order 1  
    B. Gabutti; J. N. Lyness  
    Mathematics of Computation, Vol. 39, No. 160. (Oct., 1982), pp. 587-597, Jstor.  
  19. Power Series for Practical Purposes  
    Ralph Boas  
    The Two-Year College Mathematics Journal, Vol. 13, No. 3. (Jun., 1982), pp. 191-195, Jstor.  
  20. Deducing the Properties of Singularities of Functions From Their Taylor Series Coefficients  
    C. Hunter; B. Guerrieri  
    SIAM Journal on Applied Mathematics, Vol. 39, No. 2. (Oct., 1980), pp. 248-263, Jstor.  
  21. Boundary Values of Absolutely Convergent Taylor Series  
    Aharon Atzmon  
    The Annals of Mathematics, 2nd Ser., Vol. 111, No. 2. (Mar., 1980), pp. 231-237, Jstor.  
  22. Matrix transformations of univalent power series.
    Hartmann, F. W.; MacGregor, T. H.
    J. Austral. Math. Soc. 18 (1974), 419--435, MathSciNet.  
  23. On the Zeros of Power Series with Hadamard Gaps--Distribution in Sectors  
    I-Lok Chang  
    Transactions of the American Mathematical Society, Vol. 178. (Apr., 1973), pp. 393-400, Jstor.  
  24. Formal Power Series  
    Ivan Niven  
    American Mathematical Monthly, Vol. 76, No. 8. (Oct., 1969), pp. 871-889, Jstor.  
  25. A New Method for Generating Power Series Expansions of Functions  
    J. Abate; H. Dubner  
    SIAM Journal on Numerical Analysis, Vol. 5, No. 1. (Mar., 1968), pp. 102-112, Jstor.  
  26. Definition of Radius of Convergence (in Classroom Notes)  
    D. E. Myers  
    American Mathematical Monthly, Vol. 74, No. 5. (May, 1967), pp. 586-587, Jstor.  
  27. A Proof of the Power Series Expansion Without Differentiation Theory  
    A. J. Macintyre; W. John Wilbur  
    Proceedings of the American Mathematical Society, Vol. 18, No. 3. (Jun., 1967), pp. 419-424, Jstor.  
  28. On Convergence Properties of Sequences of Analytic Functions  
    D. A. Hejhal  
    American Mathematical Monthly, Vol. 74, No. 10. (Dec., 1967), pp. 1208-1211, Jstor.  
  29. On the Convergence of Taylor Series for Functions of n Variables  
    James Thomas Day  
    Mathematics Magazine, Vol. 40, No. 5. (Nov., 1967), pp. 258-260, Jstor.  
  30. On the Coefficients and the Growth of Gap Power Series  
    Dieter Gaier  
    SIAM Journal on Numerical Analysis, Vol. 3, No. 2. (Jun., 1966), pp. 248-265, Jstor.  
  31. Power Series Whose Sections Have Zeros of Large Modulus  
    J. D. Buckholtz  
    Transactions of the American Mathematical Society, Vol. 117. (May, 1965), pp. 157-166, Jstor.  
  32. On Sequences of Power Series with Restricted Coefficients (in Classroom Notes)  
    O. Shisha  
    American Mathematical Monthly, Vol. 72, No. 5. (May, 1965), pp. 533-537, Jstor.  
  33. Generalized Taylor Series and Orders and Types of Entire Functions of Several Complex Variables  
    Fred Gross  
    Transactions of the American Mathematical Society, Vol. 120, No. 1. (Oct., 1965), pp. 124-144, Jstor.  
  34. Expansion of Analytic Functions in Infinite Series and Infinite Products with Application to Multiple Valued Functions  
    Alexander Arcache  
    American Mathematical Monthly, Vol. 72, No. 8. (Oct., 1965), pp. 861-864, Jstor.  
  35. Note on Multiple Power Series (in Classroom Notes)  
    I. M. Sheffer  
    American Mathematical Monthly, Vol. 70, No. 3. (Mar., 1963), pp. 309-313, Jstor.  
  36. Reversion of Power Series (in Classroom Notes)  
    R. M. Redheffer  
    American Mathematical Monthly, Vol. 69, No. 5. (May, 1962), pp. 423-425, Jstor.  
  37. An Algorithm of J. Schur and the Taylor Series  
    E. H. Connell; P. Porcelli  
    Proceedings of the American Mathematical Society, Vol. 13, No. 2. (Apr., 1962), pp. 232-235, Jstor.  
  38. Functional Composition Patterns and Power Series Reversion  
    George N. Raney  
    Transactions of the American Mathematical Society, Vol. 94, No. 3. (Mar., 1960), pp.  441-451, Jstor.  
  39. Power Series having Partial Sums with Zeros in a Half-Plane  
    Albert Edrei  
    Proceedings of the American Mathematical Society, Vol. 9, No. 2. (Apr., 1958), pp. 320-324, Jstor.  
  40. On a Property of Complex Power Series (in Mathematical Notes)  
    K. F. Moppert  
    American Mathematical Monthly, Vol. 64, No. 2. (Feb., 1957), pp. 88-89, Jstor.  
  41. A Theorem on Power Series Whose Coefficients Have Given Signs  
    W. H. J. Fuchs  
    Proceedings of the American Mathematical Society, Vol. 8, No. 3. (Jun., 1957), pp. 443-449, Jstor.  
  42. Power Series Expansions for Inverse Functions  
    J. S. Frame  
    American Mathematical Monthly, Vol. 64, No. 4. (Apr., 1957), pp. 236-240, Jstor.  
  43. Mean Value Theorems and Taylor Series (in Teaching of Mathematics)  
    M. R. Spiegel  
    Mathematics Magazine, Vol. 29, No. 5. (May - Jun., 1956), pp. 263-266, Jstor.  
  44. A Theorem on the Remainder of a Taylor Series (in Classroom Notes)  
    G. Rudinger  
    American Mathematical Monthly, Vol. 57, No. 6. (Jun. - Jul., 1950), pp. 411-412, Jstor.  
  45. An Integral Test for Convergence (in Mathematical Notes)  
    R. P. Agnew; R. P. Boas, Jr.  
    American Mathematical Monthly, Vol. 56, No. 10. (Dec., 1949), pp. 677-678, Jstor.  
  46. A Generalized Integral Test for Convergence of Series (in Mathematical Notes)  
    Morgan Ward  
    American Mathematical Monthly, Vol. 56, No. 3. (Mar., 1949), pp. 170-172, Jstor.  
  47. Summability of Power Series  
    R. P. Agnew  
    American Mathematical Monthly, Vol. 53, No. 5. (May, 1946), pp. 251-259, Jstor.  
  48. Power Series with Bounded Coefficients  
    R. J. Duffin; A. C. Schaeffer  
    American Journal of Mathematics, Vol. 67, No. 1. (Jan., 1945), pp. 141-154, Jstor.  
  49. Univalent Power Series with Multiply Monotonic Sequences of Coefficients  
    M. S. Robertson  
    The Annals of Mathematics, 2nd Ser., Vol. 46, No. 4. (Oct., 1945), pp. 533-555, Jstor.  
  50. Moduli of the Roots of Polynomials and Power Series  
    Louis Weisner  
    American Mathematical Monthly, Vol. 48, No. 1. (Jan., 1941), pp. 33-36, Jstor.  
  51. On the Growth Properties of a Function of Two Complex Variables Given by Its Power Series Expansion  
    Abe Gelbart  
    Transactions of the American Mathematical Society, Vol. 49, No. 2. (Mar., 1941), pp. 199-210, Jstor.  
  52. Expansions of Analytic Functions  
    R. P. Boas, Jr  
    Transactions of the American Mathematical Society, Vol. 48, No. 3. (Nov., 1940), pp. 467-487, Jstor.  
  53. On Simultaneous Expansions of Analytic Functions in Composite Power Series  
    A. C. Burdette  
    American Journal of Mathematics, Vol. 61, No. 2. (Apr., 1939), pp. 295-302, Jstor.  
  54. Note on Power Series with Big Gaps  
    M. Kac  
    American Journal of Mathematics, Vol. 61, No. 2. (Apr., 1939), pp. 473-476, Jstor.  
  55. Analytic Continuation of Diagonals and Hadamard Compositions of Multiple Power Series  
    R. H. Cameron; W. T. Martin  
    Transactions of the American Mathematical Society, Vol. 44, No. 1. (Jul., 1938), pp. 1-7, Jstor.  
  56. Expansion of Analytic Functions into Infinite Products  
    S. Borofsky  
    The Annals of Mathematics, 2nd Ser., Vol. 32, No. 1. (Jan., 1931), pp. 23-36, Jstor.  
  57. On the Expansion of Analytic Functions of the Complex Variable in Generalized Taylor's Series
    D. V. Widder
    Transactions of the American Mathematical Society, Vol. 31, No. 1. (Jan., 1929), pp. 43-52, Jstor.  
  58. Note on the Expansion of Analytic Functions in Series of Polynomials and in Series of Other Analytic Functions  
    J. L. Walsh  
    Transactions of the American Mathematical Society, Vol. 31, No. 1. (Jan., 1929), pp. 53-57, Jstor.  
  59. On Taylor's Series Admitting the Circle of Convergence as a Singular Curve  
    J. J. Gergen; D. V. Widder  
    American Journal of Mathematics, Vol. 50, No. 1. (Jan., 1928), pp. 139-146, Jstor.  
  60. On the Power Series for log (1 + z)  
    T. H. Gronwall
    The Annals of Mathematics, 2nd Ser., Vol. 18, No. 2. (Dec., 1916), pp. 70-73, Jstor.  
  61. On the Analytic Extension of Functions Defined by Double Power Series  
    W. B. Ford  
    Transactions of the American Mathematical Society, Vol. 7, No. 2. (Apr., 1906), pp. 260-274, Jstor.  
  62. On a Criterion of Pringsheim's for Expansibility in Taylor's Series  
    M. B. Porter  
    The Annals of Mathematics, 2nd Ser., Vol. 8, No. 1. (Oct., 1906), pp. 45-48, Jstor.  

 

 

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