Bibliography for Geometric Series

unabridged

 

  1. A sequence of generalizations of the geometric series
    Wunsche A.
    Journal of Computational and Applied Mathematics, v 153, n 1-2, Apr 1, 2003, p 533-534, Ingenta.  
  2. On the optimality of the geometric sequences for the m ray search.
    Gal, Shmuel
    Oper. Res. 50 (2002), no. 4, 745, MathSciNet.  
  3. A quick method for estimating generalized geometric series distribution.  
    Hassan, A.; Mishra, A.; Jan, T. R.
    Studia Sci. Math. Hungar.  39  (2002),  no. 3-4, 291--295, MathSciNet.  
  4. Tension in generalized geometric sequences  
    Goldbloom Bloch, Bill
    College Math. J. 32 (2001), no. 1, 44--47, Jstor.  
  5. On correlations of a family of generalized geometric sequences.  
    Sun, Wei; Klapper, Andrew; Yang, Yi Xian
    IEEE Trans. Inform. Theory  47  (2001),  no. 6, 2609--2618, MathSciNet.  
  6. The power integral and the geometric series.
    Wiener, Joseph; Paredes, Miguel
    Missouri J. Math. Sci. 13 (2001), no. 1, 29--35, MathSciNet.  
  7. On a quasi geometric series distribution.
    Mishra, A.; Singh, S. K.
    Aligarh J. Statist. 20 (2000), 45--56, MathSciNet.  
  8. Geometric series bounds for the local errors of Taylor methods for linear n-th order ODEs.
    Neher, Markus
    Symbolic algebraic methods and verification methods (Dagstuhl, 1999), 183--193, Springer, Vienna, 2001, MathSciNet.  
  9. Digital redesign of continuous-time state-feedback controller using the scaling and squaring geometric-series approximation method
    Tsai, Jason Sheng-Hong; Hsiao, Chien-Yao; Shieh, Leang San
    Journal of the Chinese Institute of Electrical Engineering, Transactions of the Chinese Institute of Engineers, Series E/Chung KuoTien Chi Kung Chieng Hsueh K'an, v 6, n 3, Aug, 1999, p 219-230, Compendex.  
  10. On the cross-correlations between geometric and pseudo-generalized geometric sequences. (Chinese)
    Sun, Wei; Yang, Yi Xian
    Acta Math. Appl. Sinica 22 (1999), no. 3, 327--336, MathSciNet.  
  11. The Geometric Series in Calculus  
    Andrews, G. E.
    American Mathematical Monthly, v 105, n 1, 1998, p 36--40, Jstor.
  12. A curious problem involving geometric series.
    Filipponi, Piero
    Notes Number Theory Discrete Math. 3 (1997), no. 1, 35--40, MathSciNet.  
  13. Geometric sequences of discs in the Apollonian packing.
    Aharonov, D.; Stephenson, K.
    Algebra i Analiz 9 (1997), no. 3, 104--140; translation in St. Petersburg Math. J. 9 (1998), no. 3, 509--542, MathSciNet.
  14. The analogy between periodic continued fractions & geometric series.
    Gill, John
    Comm. Anal. Theory Contin. Fractions 6 (1997), 83--88, MathSciNet.  
  15. Pade approximants and noise: A case of geometric series
    Gilewicz J.; Pindor M.
    Journal of Computational and Applied Mathematics, 23 December 1997, vol. 87, no. 2, pp. 199-214(16), Ingenta.  
  16. On the convergence of a class of random geometric series with application to random walks and percolation theory
    Kearney M.J.; Dwyer V.M.; Bressloff P.C.
    Journal of Physics A: Mathematical and General, 1997, vol. 30, no. 12, pp. L409-L414(1), Ingenta.  
  17. Correlation functions of a family of generalized geometric sequences.
    Sun, Wei; Yang, Yi Xian
    Discrete Appl. Math. 80 (1997), no. 2-3, 193--201, MathSciNet.  
  18. Model conversion of continuous-time uncertain systems via the interval geometric-series method
    Shieh, Leang-San; Zou, Xiang; Tsai, Jason S.H.
    IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, v 43, n 10, Oct, 1996, p 851-854, Compendex.  
  19. Model conversions of uncertain linear time-delay systems using a scaling and squaring geometric series method.
    Tsai, J. S. H.; Liu, F.-C.; Shieh, L.-S.; Wei, C.-P.
    Control Theory Adv. Tech. 10 (1995), no. 4, part 5, 2145--2171, MathSciNet.  
  20. Model conversions of uncertain linear systems using a scaling and squaring geometric series method
    Shieh, Leang S.; Gu, Jingfong; Tsai, Jason S.H.
    Circuits, Systems, and Signal Processing, v 14, n 4, 1995, p 445-463, Compendex.  
  21. Proof without Words: Geometric Series  
    Sunday A. Ajose; Roger B. Nelsen  
    Mathematics Magazine, Vol. 67, No. 3. (Jun., 1994), p. 230, Jstor.  
  22. Partial period autocorrelations of geometric sequences.
    Klapper, Andrew M.; Goresky, Mark
    IEEE Trans. Inform. Theory 40 (1994), no. 2, 494--502, MathSciNet.  
  23. The vulnerability of geometric sequences based on fields of odd characteristic.
    Klapper, Andrew
    J. Cryptology 7 (1994), no. 1, 33--51, MathSciNet.  
  24. On a characteristic of the geometric series distribution.
    Mishra, A.; Singh, S. K.
    J. Bihar Math. Soc. 15 (1992), 32--35 (1994), MathSciNet.  
  25. A Law of the Iterated Logarithm for Random Geometric Series  
    Anton Bovier; Pierre Picco  
    The Annals of Probability, Vol. 21, No. 1. (Jan., 1993), pp. 168-184, Jstor.  
  26. Proof without Words: Geometric Series (in Notes)  
    Elizabeth M. Markham  
    Mathematics Magazine, Vol. 66, No. 4. (Oct., 1993), p. 242, Jstor.  
  27. Summing geometric series recursively
    Mathews, John H.
    Math. Comput. Ed. 27 (1993), no. 2, 125--134, MathSciNet.  
  28. A law of the iterated logarithm for random geometric series.
    Bovier, Anton; Picco, Pierre
    Ann. Probab. 21 (1993), no. 1, 168--184, MathSciNet.  
  29. Matrix transformations of classes of geometric sequences.
    Selvaraj, C. R.; Selvaraj, Suguna
    Rocky Mountain J. Math. 23 (1993), no. 3, 1099--1106, MathSciNet.  
  30. Cross-correlations of linearly and quadratically related geometric sequences and GMW sequences.
    Klapper, A.; Chan, A. H.; Goresky, M.
    Discrete Appl. Math. 46 (1993), no. 1, 1--20, MathSciNet.  
  31. Cross-correlations of geometric sequences in characteristic two.
    Klapper, A.
    Des. Codes Cryptogr. 3 (1993), no. 4, 347--377, MathSciNet.  
  32. The vulnerability of geometric sequences based on fields of odd characteristic (extended abstract).
    Klapper, Andrew
    Advances in cryptology---AUSCRYPT '92 (Gold Coast, 1992), 327--338, Lecture Notes in Comput. Sci., 718, Springer, Berlin, 1993, MathSciNet.  
  33. Summing Geometric Series by Holding a Tournament (in Classroom Capsules)  
    Vincent P. Schielack, Jr.  
    The College Mathematics Journal, Vol. 23, No. 3. (May, 1992), pp. 210-211, Jstor.  
  34. Matrix summability of classes of geometric sequences.
    Selvaraj, Suguna
    Rocky Mountain J. Math. 22 (1992), no. 2, 719--732, MathSciNet.  
  35. The distribution functions of certain random geometric series concerning intersymbol interference.
    Smith, Peter J.
    IEEE Trans. Inform. Theory 37 (1991), no. 6, 1657--1662, MathSciNet.  
  36. Correlation functions of geometric sequences.
    Chan, Agnes Hui; Goresky, Mark; Klapper, Andrew
    Advances in cryptology---EUROCRYPT '90 (Aarhus, 1990), 214--221, Lecture Notes in Comput. Sci., 473, Springer, Berlin, 1991, MathSciNet.  
  37. Fonctions entières prenant des valeurs presque entières aux points d'une progression géométrique. (French) [Entire functions assuming almost integer values in a geometric sequence]
    Bézivin, Jean-Paul
    Monatsh. Math. 110 (1990), no. 1, 3--13, MathSciNet.  
  38. Proof without Words: Differentiated Geometric Series (in Notes)  
    Roger B. Nelsen  
    Mathematics Magazine, Vol. 62, No. 5. (Dec., 1989), pp. 332-333, Jstor.  
  39. A new generalisation of geometric series distribution.
    Mishra, Amarendra; Singh, Shreekant
    J. Bihar Math. Soc. 12 (1989), 53--60, MathSciNet.  
  40. On entire functions assuming integer values in a geometric sequence  
    Wallisser, R. V.
    Théorie des nombres (Quebec, PQ, 1987), 981--989, de Gruyter, Berlin, 1989, MathSciNet.  
  41. Généralisation de la série géométrique et applications. (French) [Generalization of geometric series, and applications]
    Dubeau, François; Savoie, Jean
    Ann. Sci. Math. Québec 11 (1987), no. 2, 305--320, MathSciNet.  
  42. Über die geometrische Reihe von E. Hecke. (German) [On the geometric series of E. Hecke]
    Hlawka, Edmund
    Acta Arith. 49 (1987), no. 2, 113--125, MathSciNet.  
  43. Geometric Series and a Probability Problem (in Notes)  
    Curtis Cooper  
    The American Mathematical Monthly, Vol. 93, No. 2. (Feb., 1986), pp. 126-127, Jstor.  
  44. Geometrische Reihen in algebraischen Zahlkörpern. (German) [Geometric series in algebraic number fields]
    Rausch, Ulrich
    Acta Arith. 47 (1986), no. 4, 313--345, MathSciNet.  
  45. Über ganze Funktionen, die in einer geometrischen Folge ganze Werte annehmen. (German) [On entire functions assuming integer values in a geometric sequence]
    Wallisser, Rolf
    Monatsh. Math. 100 (1985), no. 4, 329--335, MathSciNet.  
  46. Geometric Series in Incomplete Normed Algebras (in Notes)  
    R. Fuster; A. Marquina  
    The American Mathematical Monthly, Vol. 91, No. 1. (Jan., 1984), pp. 49-51, Jstor.  
  47. Orthonormal geometric sequences and their L transforms.
    Ku's, Stanislaw
    Demonstratio Math. 17 (1984), no. 3, 647--654 (1985), MathSciNet.  
  48. Closed-Form Formulas for Quasi-Geometric Series  
    Arthur C. Segal  
    The Two-Year College Mathematics Journal, Vol. 14, No. 2. (Mar., 1983), pp. 118-122, Jstor.  
  49. A regular summability method which sums the geometric series to its proper value in the whole complex plane
    Tomm, Ludwig
    Canad. Math. Bull. 26 (1983), no. 2, 179--180, MathSciNet.  
  50. A summability approximation theorem for the transforms of the geometric series.
    Tomm, Ludwig
    J. Approx. Theory 39 (1983), no. 3, 247--258, MathSciNet.  
  51. The Carathéodory-Fejér extension of a finite geometric series.
    Ellacott, S. W.; Gutknecht, M. H.
    IMA J. Numer. Anal. 3 (1983), no. 2, 221--227, MathSciNet.  
  52. A generalisation of geometric series distribution.
    Mishra, Amarendra
    J. Bihar Math. Soc. 6 (1982), 18--22, MathSciNet.  
  53. Universelle Approximation durch Riesz-Transformierte der geometrischen Reihe. (German) [Universal approximation by using the Riesz transform of the geometric series]
    Faulstich, Karin; Luh, Wolfgang; Tomm, Ludwig
    Manuscripta Math. 36 (1981/82), no. 3, 309--321, MathSciNet.  
  54. An Investment Approach to Geometric Series (in Classroom Capsules)  
    Robert Donaghey; Warren Gordon  
    The Two-Year College Mathematics Journal, Vol. 11, No. 2. (Mar., 1980), pp. 120-121, Jstor.  
  55. Zipf's Law
    Philip M. Tuchinsky
    Consortium for Mathematics and Its Applications, (1980) Lexington, MA, COMAP.  
  56. A geometric series approach for approximation of transition matrices in quadratic synthesis.
    Shieh, L. S.; Wai, W. B.; Yates, R. E.
    Trans. ASME Ser. G J. Dynamic Systems Measurement Control 102 (1980), no. 3, 193--197, MathSciNet.  
  57. Geometric Series on the Gridiron (in Mathematical)  
    Andris Niedra  
    The Two-Year College Mathematics Journal, Vol. 9, No. 1. (Jan., 1978), pp. 18-20, Jstor.  
  58. Geometric sequences and the initial digit problem.
    Whitney, Raymond E.
    Fibonacci Quart. 16 (1978), no. 2, 152--154, MathSciNet.  
  59. A Note on the Geometric Series as a Species Frequency Model (in Miscellanea)  
    Steinar Engen  
    Biometrika, Vol. 62, No. 3. (Dec., 1975), pp. 697-699, Jstor.  
  60. A note on the geometric series as a species frequency model.
    Engen, Steiner
    Biometrika 62 (1975), no. 3, 697--699, MathSciNet.  
  61. A certain generalization of the geometric series. (Bulgarian)  
    Kondev, N. M.
    Godisnik Visvs. Tehn. Ucebn. Zaved. Mat.  8  (1972), no. 2, 45--48 (1973), MathSciNet.  
  62. Elementary Geometric/Arithmetic Series and Early Production Theory  
    Peter J. Lloyd  
    The Journal of Political Economy, Vol. 77, No. 1. (Jan. - Feb., 1969), pp. 21-34, Jstor.  
  63. Representation of real numbers by generalized geometric series.
    Maier, E. A.
    Pacific J. Math. 28 1969 603--609, MathSciNet.  
  64. New Geometric Representation of an Old Infinite Series (in Classroom Notes)  
    A. Feingold  
    The American Mathematical Monthly, Vol. 73, No. 5. (May, 1966), pp. 528-531, Jstor.  
  65. Cardinality of Level Sets of Rademacher Series Whose Coefficients form a Geometric Progression  
    W. A. Beyer  
    Proceedings of the American Mathematical Society, Vol. 13, No. 4. (Aug., 1962),  pp. 579-584, Jstor.  
  66. On a Generlization of the Geometric Series (in Mathematical Notes)  
    M. S. Klamkin  
    The American Mathematical Monthly, Vol. 64, No. 2. (Feb., 1957), pp. 91-93, Jstor.  
  67. On the arithmetico-geometric series
    Carr, A. J.
    Math. Gaz. 41 (1957), 44--46, MathSciNet.  
  68. Mapping properties of Cesàro sums of order two of the geometric series.
    Rauch, S. E.
    Pacific J. Math. 4, (1954). 109--121, MathSciNet.  
  69. The partial sums of second order of the geometric series.
    Schweitzer, M.
    Duke Math. J. 18, (1951). 527--533, MathSciNet.  
  70. A Generalization of the Geometric Series  
    Robert Stalley  
    The American Mathematical Monthly, Vol. 56, No. 5. (May, 1949), pp. 325-327, Jstor.  
  71. On certain transformations in generalized hyper-geometric series.
    Bose, B. N.
    Bull. Calcutta Math. Soc. 36, (1944). 74--79, MathSciNet.  
  72. Geometric Examples of Convergent Series  
    C. A. Barnhart  
    National Mathematics Magazine, Vol. 17, No. 4. (Jan., 1943), pp. 159-162, Jstor.  
  73. Comments Concerning "A Note on Observed Geometric Series" by A. B. Soble in the April, 1940 Issue  
    William Dowell Baten; A. B. Soble  
    National Mathematics Magazine, Vol. 16, No. 2. (Nov., 1941), pp. 62-63, Jstor.  
  74. Geometric Discussion of the Absolute Convergence of a Series with Complex Terms  
    George H. Ling  
    The Annals of Mathematics, 2nd Ser., Vol. 5, No. 3. (Apr., 1904), pp. 151-152, Jstor.  
  75. Note on Integral and Integro-Geometric Series  
    Edward Drake Roe  
    The Annals of Mathematics, Vol. 11, No. 1/6. (1896 - 1897), pp. 184-194, Jstor.  

 

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