Bibliography for Convergence of Series

unabridged

 

  1. A new theorem on convergence of positive series and its application. (Chinese)
    Hong, Yong
    Sichuan Shifan Daxue Xuebao Ziran Kexue Ban 27 (2004), no. 3, 245--247.
  2. Statistical convergence of infinite series.
    Dindo\v s, M.; \v Salát, T.; Toma, V.
    Czechoslovak Math. J. 53(128) (2003), no. 4, 989--1000.
  3. The series of complex fuzzy number and complex fuzzy-valued functions and its convergence.
    Shengquan, Ma; Gong, Zengtai
    Int. J. Pure Appl. Math. 7 (2003), no. 1, 49--62.
  4. On the convergence of fuzzy number series. (Chinese)
    Zhang, Ji Guo; Zhu, Yong Zhong; Zhang, Wen Xiu
    Mohu Xitong yu Shuxue 17 (2003), no. 1, 66--72.
  5. Convergence and formal manipulation of series from the origins of calculus to about 1730
    Ferraro, Giovanni
    Annals of Science, v 59, n 2, April, 2002, p 179-199, Compendex.  
  6. A further discussion on the complex fuzzy series and their convergence. (Chinese)
    Ma, Sheng Quan
    Mohu Xitong yu Shuxue 16 (2002), no. 2, 92--96.
  7. Convergence and summation of bi-alternating series. (Chinese)
    Zheng, Ji Ming; Tang, Xing Li
    J. Chongqing Norm. Univ. Nat. Sci. Ed. 19 (2002), no. 1, 33--34.
  8. Pointwise convergence of Fourier series.
    Arias-de-Reyna, J.
    J. London Math. Soc. (2) 65 (2002), no. 1, 139--153.
  9. Convergence-Divergence of p-Series  
    Rasul A. Khan
    The College Mathematics Journal, Vol. 32, No. 3 (May, 2001), pp. 206-208, Jstor.   
  10. Convergence of Fourier series and Gibbs phenomenon
    Xiong, Y.X.; Liu, D.C.
    Wuhan Daxue Xuebao (Gongxue Ban)/Engineering Journal of Wuhan University, v 34, n 1, February, 2001, p 69 Language: Chinese, Compendex.  
  11. On the restudy of fuzzy complex analysis: Part I. the sequence and series of fuzzy complex numbers and their convergences
    Qiu, Jiqing ; Wu, Congxin; Li, Fachao
    Fuzzy Sets and Systems, v 115, n 3, Nov 1, 2000, p 445-450, Compendex.  
  12. Olivier and Abel on Series Convergence: An Episode from Early 19th Century Analysis  
    Michael Goar
    Mathematics Magazine,  Vol. 72, No. 5 (Dec., 1999), pp. 347-355, Jstor.   
  13. Proof without Words: An Alternating Series (in Notes)  
    James O. Chilaka  
    Mathematics Magazine, Vol. 69, No. 5. (Dec., 1996), pp. 355-356, Jstor.  
  14. Kummer's Test Gives Characterizations for Convergence or Divergence of all Positive Series  
    Jingcheng Tong
    The American Mathematical Monthly, Vol. 101, No. 5 (May, 1994), pp. 450-452, Jstor.   
  15. A New (?) Test for Convergence of Series (in Notes)  
    K. P. S. Bhaskara Rao  
    Mathematics Magazine, Vol. 67, No. 4. (Oct., 1994), pp. 301-302, Jstor.  
  16. Calculating Sums of Infinite Series  
    Bart Braden  
    The American Mathematical Monthly, Vol. 99, No. 7. (Aug. - Sep., 1992), pp. 649-655, Jstor.  
  17. The Radius of Convergence of Power Series Solutions to Linear Differential Equations (in The Teaching of Mathematics)  
    Isom H. Herron  
    The American Mathematical Monthly, Vol. 96, No. 9. (Nov., 1989), pp. 824-827, Jstor.  
  18. Evaluating the Sum of the Series (in Classroom Capsules)  
    Alan Gorfin  
    The College Mathematics Journal, Vol. 20, No. 4. (Sep., 1989), pp. 329-331, Jstor.  
  19. Estimating the Sum of Alternating Series  
    James D. Harper  
    The College Mathematics Journal, Vol. 19, No. 2. (Mar., 1988), pp. 149-153, Jstor.  
  20. Summation of Infinite Series Related to Roots of Certain Functions
    Lee, Sanboh, and J. C. M. Li
    Int. J. of Math. Ed. in Sci. and Tech., V. 19, No. 1, (1988), pp. 89-93.
  21. A Simple Proof of Series Convergence  
    A. R. Amir-Moez
    The College Mathematics Journal, Vol. 18, No. 5 (Nov., 1987), p. 410, Jstor.   
  22. N! and the Root Test (in The Teaching of Mathematics)  
    Charles C. Mumma II  
    The American Mathematical Monthly, Vol. 93, No. 7. (Aug. - Sep., 1986), p. 561, Jstor.  
  23. A Note on Alternating Series in Several Dimensions  
    David Borwein; Jonathan M. Borwein  
    The American Mathematical Monthly, Vol. 93, No. 7. (Aug. - Sep., 1986), pp. 531-539, Jstor.  
  24. The Interval of Convergence and Limiting Functions of a Hyperpower Sequence  
    J. M. De Villiers; P. N. Robinson  
    The American Mathematical Monthly, Vol. 93, No. 1. (Jan., 1986), pp. 13-23, Jstor.  
  25. Counterexamples to a Comparison Test for Alternating Series (in Classroom Capsules)  
    J. Richard Morris  
    The College Mathematics Journal, Vol. 17, No. 2. (Mar., 1986), pp. 165-166, Jstor.  
  26. Diophantine Approximation and Convergence of Alternating Series  
    N. V. Rao  
    Proceedings of the American Mathematical Society, Vol. 93, No. 3. (Mar., 1985), pp. 420-422, Jstor.  
  27. Rates of convergence for tail series
    Tomkins, R. J.
    Journal of Statistical Planning and Inference, v 43, n 1-2, 1995, p 77, Compendex.  
  28. An Alternative to the Integral Test (in Notes)  
    Gerald Jungck  
    Mathematics Magazine, Vol. 56, No. 4. (Sep., 1983), pp. 232-235.
  29. Modified Convergence of Taylor Series  
    Robert D. Small
    The American Mathematical Monthly, Vol. 88, No. 6 (Jun., 1981), pp. 439-441, Jstor.   
  30. Rearranging Terms in Alternating Series (in Notes)  
    Richard Beigel  
    Mathematics Magazine, Vol. 54, No. 5. (Nov., 1981), pp. 244-246, Jstor.  
  31. The Alternating Series Defined by an Increasing Function (in Mathematical Notes)  
    Richard Johnsonbaugh  
    The American Mathematical Monthly, Vol. 87, No. 1. (Jan., 1980), pp. 36-38, Jstor.  
  32. The Convergence and Partial Convergence of Alternating Series  
    J. R. Philip  
    Mathematics of Computation, Vol. 35, No. 151. (Jul., 1980), pp. 907-916, Jstor.  
  33. Pointwise Convergence of Fourier Series  
    Paul R. Chernoff
    The American Mathematical Monthly, Vol. 87, No. 5 (May, 1980), pp. 399-400, Jstor.   
  34. Summing an Alternating Series  
    Richard Johnsonbaugh  
    The American Mathematical Monthly, Vol. 86, No. 8. (Oct., 1979), pp. 637-648, Jstor.  
  35. A Note on Infinite Series (in Classroom Notes)  
    Louise S. Grinstein  
    The Two-Year College Mathematics Journal, Vol. 9, No. 1. (Jan., 1978), pp. 46-47, Jstor.  
  36. Averaging an Alternating Series (in Notes)  
    Mark A. Pinsky  
    Mathematics Magazine, Vol. 51, No. 4. (Sep., 1978), pp. 235-237, Jstor.  
  37. An Integral Test for Series and Generalized Contractions (in Mathematical Notes)  
    Mieczyslaw Altman  
    The American Mathematical Monthly, Vol. 82, No. 8. (Oct., 1975), pp. 827-829, Jstor.  
  38. An Alternative to the Integral Test for Infinite Series (in Classroom Notes)  
    G. J. Porter  
    The American Mathematical Monthly, Vol. 79, No. 6. (Jun. - Jul., 1972), pp. 634-635, Jstor.  
  39. The Intervals of Convergence of Some Power Series   
    Eugene Schenkman
    The American Mathematical Monthly, Vol. 78, No. 8 (Oct., 1971), pp. 890-892, Jstor.   
  40. A Ratio-Type Convergence Test (in Mathematical Notes)  
    H. Miller  
    The American Mathematical Monthly, Vol. 77, No. 3. (Mar., 1970), pp. 285-287, Jstor.  
  41. A Note on a Form of Ratio Test  
    S. H. L. Kung  
    Mathematics Magazine, Vol. 41, No. 3. (May, 1968), pp. 144-146, Jstor.  
  42. 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.   
  43. Definition of Radius of Convergence (in Classroom Notes)  
    D. E. Myers  
    The American Mathematical Monthly, Vol. 74, No. 5. (May, 1967), pp. 586-587, Jstor.  
  44. Some Extensions of the Integral Test (in Classroom Notes)  
    G. T. Cargo  
    The American Mathematical Monthly, Vol. 73, No. 5. (May, 1966), pp. 521-525, Jstor.  
  45. Change of Variables Test for Convergence of Series  
    Lee Yong-Jeng
    The American Mathematical Monthly, Vol. 73, No. 9 (Nov., 1966), pp. 996-997, Jstor.   
  46. On the Convergence of the Binomial Series  
    Aughtum Howard
    The American Mathematical Monthly, Vol. 73, No. 7 (Aug., 1966), pp. 760-761, Jstor.   
  47. Remark on a Nonlinear Convergence-Producing Series Transformation  
    D. L. Goldsmith
    The American Mathematical Monthly, Vol. 72, No. 5 (May, 1965), pp. 523-525, Jstor.   
  48. A Convergence Criterion for Positive Series  
    Jack P. Tull; David Rearick
    The American Mathematical Monthly, Vol. 71, No. 3 (Mar., 1964), pp. 294-295, Jstor.   
  49. A Modified MacLaurin Integral Test (in Classroom Notes)  
    Louis C. Barrett  
    The American Mathematical Monthly, Vol. 71, No. 2. (Feb., 1964), pp. 190-193, Jstor.  
  50. Concerning a Theorem of Hadamard (in Mathematical Notes)  
    David F. Dawson  
    The American Mathematical Monthly, Vol. 69, No. 10. (Dec., 1962), pp. 981-983, Jstor.  
  51. A Note on Alternating Series (in Classroom Notes)  
    Philip Calabrese  
    The American Mathematical Monthly, Vol. 69, No. 3. (Mar., 1962), pp. 215-217, Jstor.  
  52. On the Convergence of the Series  Sum n^-a  
    H. Schwerdtfeger
    The American Mathematical Monthly, Vol. 68, No. 4 (Apr., 1961), pp. 361-363, Jstor.   
  53. Note on the Convergence of Series of Ultraspherical Polynomials  
    D. P. Gupta
    The American Mathematical Monthly, Vol. 65, No. 10 (Dec., 1958), pp. 762-764, Jstor.   
  54. On the Cauchy Criterion for the Convergence of an Infinite Series  
    Albert Wilansky
    The American Mathematical Monthly, Vol. 64, No. 7 (Aug., 1957), pp. 469-471, Jstor.   
  55. Convergence of Series with Positive Terms (in Mathematical Notes)  
    E. Baylis Shanks  
    The American Mathematical Monthly, Vol. 64, No. 5. (May, 1957), pp. 338-341, Jstor.  
  56. Improving the Convergence of Series: Application to Some Elliptic Integrals  
    Leo F. Epstein; Nancy E. French
    The American Mathematical Monthly, Vol. 63, No. 10 (Dec., 1956), pp. 698-704, Jstor.   
  57. On a Convergence Test for Alternating Series  
    R. Lariviere
    Mathematics Magazine, Vol. 29, No. 2 (Nov., 1955), p. 88, Jstor.   
  58. A Note on a Generalization of the Cauchy-Maclaurin Integral Test (in Mathematical Notes)  
    T. A. Newton  
    The American Mathematical Monthly, Vol. 61, No. 5. (May, 1954), pp. 331-334, Jstor.  
  59. On the Convergence of the p-Series  
    R. M. Foster; M. S. Klamkin
    The American Mathematical Monthly, Vol. 60, No. 9 (Nov., 1953), pp. 625-626, Jstor.   
  60. On the Convergence of Alternating Double Series  
    Burnett Meyer
    The American Mathematical Monthly, Vol. 60, No. 6 (Jun., 1953), pp. 402-404, Jstor.   
  61. Some Necessary Conditions for Convergence of Infinite Series and Improper Integrals  
    M. J. Norris
    The American Mathematical Monthly, Vol. 60, No. 2 (Feb., 1953), pp. 96-97, Jstor.   
  62. An Integral Test for Convergence (in Mathematical Notes)  
    R. P. Agnew; R. P. Boas, Jr.  
    The American Mathematical Monthly, Vol. 56, No. 10. (Dec., 1949), pp. 677-678, Jstor.  
  63. A Generalized Integral Test for Convergence of Series (in Mathematical Notes)  
    Morgan Ward  
    The American Mathematical Monthly, Vol. 56, No. 3. (Mar., 1949), pp. 170-172, Jstor.  
  64. A Generalization of the Ratio Test for Series (in Classroom Notes)  
    R. J. Duffin  
    The American Mathematical Monthly, Vol. 55, No. 3. (Mar., 1948), pp. 153-155, Jstor.  
  65. Convergence of Multiply-Infinite Series  
    I. M. Sheffer
    The American Mathematical Monthly, Vol. 52, No. 7 (Aug., 1945), pp. 365-376, Jstor.   
  66. A Series Comparison Test for Calculus Students (in Questions, Discussons, and Notes)  
    Henry Scheffe  
    The American Mathematical Monthly, Vol. 48, No. 4. (Apr., 1941), pp. 256-257, Jstor.  
  67. The Ratio Test for Convergence of Series (in Questions, Discussions, and Notes)  
    N. J. Lennes  
    The American Mathematical Monthly, Vol. 46, No. 7. (Aug. - Sep., 1939), pp. 434-436, Jstor.  
  68. On the Absolute Convergence of Polynomial Series  
    Einar Hille
    The American Mathematical Monthly, Vol. 45, No. 4 (Apr., 1938), pp. 220-226, Jstor.  
  69. 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.  
  70. The Convergence of Fourier Series  
    Dunham Jackson
    The American Mathematical Monthly, Vol. 41, No. 2 (Feb., 1934), pp. 67-84, Jstor.  
  71. Simplified Integral Test for the Convergence of Infinite Series  
    Raymond W. Brink  
    The American Mathematical Monthly, Vol. 38, No. 4. (Apr., 1931), pp. 205-208, Jstor.  
  72. Discussions: Note on the Convergence of Fourier Series  
    Dunham Jackson
    The American Mathematical Monthly, Vol. 33, No. 1 (Jan., 1926), pp. 39-40, Jstor.  
  73. A New Sequence of Integral Tests for the Convergence and Divergence of Infinite Series  
    Raymond W. Brink  
    The Annals of Mathematics, 2nd Ser., Vol. 21, No. 1. (Sep., 1919), pp. 39-60, Jstor.  
  74. A New Integral Test for the Convergence and Divergence of Infinite Series  
    Raymond W. Brink  
    Transactions of the American Mathematical Society, Vol. 19, No. 2. (Apr., 1918), pp. 186-204, Jstor.  
  75. A Note on the Sum of the Remainders of a Series  
    Glenn James  
    The American Mathematical Monthly, Vol. 23, No. 9. (Nov., 1916), pp. 333-336, Jstor.  
  76. A Curious Convergent Series  
    Frank Irwin  
    The American Mathematical Monthly, Vol. 23, No. 5. (May, 1916), pp. 149-152, Jstor.  
  77. On Linear Criteria for the Determination of the Radius of Convergence of a Power Series  
    Edward B. Van Vleck  
    Transactions of the American Mathematical Society, Vol. 1, No. 3. (Jul., 1900), pp. 293-309, Jstor.  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2006