不定和分
出典: フリー百科事典『ウィキペディア（Wikipedia）』 (2015/09/27 09:25 UTC 版)
数学における不定和分（ふていわぶん、英: indefinite sum）∑x または逆差分（ぎゃくさぶん、英: antidifference; 反差分）Δ−1 [1][2][3] は、微分に対する不定積分（反微分）の離散版で、前進差分 Δ の逆演算となる線型作用素である。[注 1]
- ^ Indefinite Sum - PlanetMath.（英語）
- ^ On Computing Closed Forms for Indefinite Summations. Yiu-Kwong Man. J. Symbolic Computation (1993), 16, 355-376
- ^ "If Y is a function whose first difference is the function y, then Y is called an indefinite sum of y and denoted Δ−1y" Introduction to Difference Equations, Samuel Goldberg
- ^ Algorithms for Nonlinear Higher Order Difference Equations, Manuel Kauers
- ^ Bruce C. Berndt, Ramanujan's Notebooks, Ramanujan's Theory of Divergent Series, Chapter 6, Springer-Verlag (ed.), (1939), pp. 133–149.
- ^ Éric Delabaere, Ramanujan's Summation, Algorithms Seminar 2001–2002, F. Chyzak (ed.), INRIA, (2003), pp. 83–88.
- ^ "Handbook of discrete and combinatorial mathematics", Kenneth H. Rosen, John G. Michaels, CRC Press, 1999, ISBN 0-8493-0149-1
- ^ Bernoulli numbers of the second kind on Mathworld
- ^ Markus Müller. How to Add a Non-Integer Number of Terms, and How to Produce Unusual Infinite Summations (note that he uses a slightly alternative definition of fractional sum in his work, i.e. inverse to backwards difference, hence 1 as the lower limit in his formula)
[続きの解説]
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