Generating functions for products of recursive sequences

Author:
David Zeitlin

Journal:
Trans. Amer. Math. Soc. **116** (1965), 300-315

MSC:
Primary 40.10

DOI:
https://doi.org/10.1090/S0002-9947-1965-0185301-0

MathSciNet review:
0185301

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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**, https://doi.org/10.2307/2311808**[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****[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****[5]**Dov Jarden,*Recurring sequences: a collection of papers*, Riveon Lematematika, Jerusalem, 1958. MR**0098201****[6]**John Riordan,*Generating functions for powers of Fibonacci numbers*, Duke Math. J.**29**(1962), 5–12. MR**0132023****[7]**H. W. Gould,*A series transformation for finding convolution identities*, Duke Math. J.**28**(1961), 193–202. MR**0123895****[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**, https://doi.org/10.2307/2313063**[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**, https://doi.org/10.2307/2306513**[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**, https://doi.org/10.2307/2308950**[13]**A. Erdélyi, W. Magnus, F. Oberhettinger and F. G. Tricomi,*Higher transcendental functions*, Vol. 1, McGraw-Hill, New York, 1953.**[14]**János Surányi,*On a problem of old Chinese mathematics*, Publ. Math. Debrecen**4**(1956), 195–197. MR**0078942****[15]**L. Carlitz, Review of*On a problem of old Chinese mathematics*, Math. Reviews**18**(1957), 4.

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DOI:
https://doi.org/10.1090/S0002-9947-1965-0185301-0

Article copyright:
© Copyright 1965
American Mathematical Society