Generating functions for products of recursive sequences
Author:
David Zeitlin
Journal:
Trans. Amer. Math. Soc. 116 (1965), 300315
MSC:
Primary 40.10
MathSciNet review:
0185301
Fulltext PDF Free Access
References 
Similar Articles 
Additional Information
 [1]
David
Zeitlin, Two methods for the evaluation of
∑^{∞}_{𝑘=0}𝑘ⁿ𝑥^{𝑘},
Amer. Math. Monthly 68 (1961), 986–989. MR 0131687
(24 #A1535)
 [2]
C. Jordan, Calculus of finite differences, Chelsea, New York, 1960.
 [3]
L.
Carlitz, Generating functions for powers of certain sequences of
numbers, Duke Math. J. 29 (1962), 521–537. MR 0140476
(25 #3896)
 [4]
Dov
Jarden and Theodor
Motzkin, The product of sequences with a common linear recursion
formula of order 2, Riveon Lematematika 3 (1949),
25–27, 38 (Hebrew, with English summary). MR 0030009
(10,698f)
 [5]
Dov
Jarden, Recurring sequences: a collection of papers, Riveon
Lematematika, Jerusalem, 1958. MR 0098201
(20 #4663)
 [6]
John
Riordan, Generating functions for powers of Fibonacci numbers,
Duke Math. J. 29 (1962), 5–12. MR 0132023
(24 #A1870)
 [7]
H.
W. Gould, A series transformation for finding convolution
identities, Duke Math. J. 28 (1961), 193–202.
MR
0123895 (23 #A1216)
 [8]
L. E. Dickson, History of the theory of numbers, Vol. 1, Chelsea, New York, 1952.
 [9]
David
Zeitlin, On identities for Fibonacci numbers, Amer. Math.
Monthly 70 (1963), 987–991. MR 0155789
(27 #5723)
 [10]
I. J. Schwatt, An introduction to the operations with series, Chelsea, New York, 1962.
 [11]
Leonard
Carlitz, Note on a paper of Shanks, Amer. Math. Monthly
59 (1952), 239–241. MR 0047595
(13,899g)
 [12]
F.
H. Northover, R.
C. Read, and Immanuel
Marx, Advanced Problems and Solutions: Solutions: 4835, Amer.
Math. Monthly 67 (1960), no. 1, 89. MR
1530597, http://dx.doi.org/10.2307/2308950
 [13]
A. Erdélyi, W. Magnus, F. Oberhettinger and F. G. Tricomi, Higher transcendental functions, Vol. 1, McGrawHill, New York, 1953.
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János
Surányi, On a problem of old Chinese mathematics, Publ.
Math. Debrecen 4 (1956), 195–197. MR 0078942
(18,4b)
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L. Carlitz, Review of On a problem of old Chinese mathematics, Math. Reviews 18 (1957), 4.
 [1]
 D. Zeitlin, Two methods for the evaluation of , Amer. Math. Monthly 68 (1961), 986989. MR 0131687 (24:A1535)
 [2]
 C. Jordan, Calculus of finite differences, Chelsea, New York, 1960.
 [3]
 L. Carlitz, Generating functions for powers of certain sequences of numbers, Duke Math. J. 29 (1962), 521538. MR 0140476 (25:3896)
 [4]
 D. Jarden and T. Motzkin, The product of sequences with a common linear recursion formula of order 2, Riveon Lematematika 3 (1949), 2527, 38. (Hebrew. English summary) MR 0030009 (10:698f)
 [5]
 D. Jarden, Recurring sequences; a collection of papers, Riveon Lematematika, Jerusalem, 1958. MR 0098201 (20:4663)
 [6]
 J. Riordan, Generating functions for powers of Fibonacci numbers, Duke Math. J. 29 (1962), 512. MR 0132023 (24:A1870)
 [7]
 H. W. Gould, A series transformation for finding convolution identities, Duke Math. J. 28 (1961), 193202. MR 0123895 (23:A1216)
 [8]
 L. E. Dickson, History of the theory of numbers, Vol. 1, Chelsea, New York, 1952.
 [9]
 D. Zeitlin, On identities for Fibonacci numbers, Amer. Math. Monthly 70 (1963), 987991. MR 0155789 (27:5723)
 [10]
 I. J. Schwatt, An introduction to the operations with series, Chelsea, New York, 1962.
 [11]
 L. Carlitz, Note on a paper of Shanks, Amer. Math. Monthly 59 (1952), 239241. MR 0047595 (13:899g)
 [12]
 I. Marx, Problem 4835, Amer. Math. Monthly 67 (1960), 89. MR 1530597
 [13]
 A. Erdélyi, W. Magnus, F. Oberhettinger and F. G. Tricomi, Higher transcendental functions, Vol. 1, McGrawHill, New York, 1953.
 [14]
 J. Surányi, On a problem of old Chinese mathematics, Publ. Math. Debrecen 4 (1956), 195197. MR 0078942 (18:4b)
 [15]
 L. Carlitz, Review of On a problem of old Chinese mathematics, Math. Reviews 18 (1957), 4.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947196501853010
PII:
S 00029947(1965)01853010
Article copyright:
© Copyright 1965
American Mathematical Society
