Singularities of a class of meromorphic functions
Authors:
Nicholas P. Callas and W. J. Thron
Journal:
Proc. Amer. Math. Soc. 33 (1972), 445454
MSC:
Primary 30A22; Secondary 30A68
MathSciNet review:
0291420
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Additional Information
Abstract: Estimates are obtained for the number of singular points, which are not poles, lying on the unit circle of the complex plane of a class of meromorphic functions which are represented by Cfractions.
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 [1]
 N. P. Callas and W. J. Thron, Singularities of meromorphic functions represented by regular Cfractions, Norske Vid. Selsk. Skr. (Trondheim) 1967, no. 6. MR 36 #6595. MR 0223547 (36:6595)
 [2]
 , Singular points of certain functions represented by Cfractions, i. Indian Math. Soc. 32 (1968), suppl. 1, 325353. MR 0291419 (45:512)
 [3]
 Kari Hag, A theorem on Tfractions corresponding to a rational function, Proc. Amer. Math. Soc. 25 (1970), 247253. MR 41 #3723. MR 0259081 (41:3723)
 [4]
 Thomas H. Jefferson, Truncation error estimates for Tfractions, SIAM J. Numer. Anal. 6 (1969), 359364. MR 41 #4775. MR 0260147 (41:4775)
 [5]
 William B. Jones and W. J. Thron, Further properties of Tfractions, Math. Ann. 166 (1966), 106118. MR 34 #319. MR 0200425 (34:319)
 [6]
 Walter Leighton and W. T. Scott, A general continued fraction expansion, Bull. Amer. Math. Soc. 45 (1939), 596605. MR 1, 7. MR 0000041 (1:7f)
 [7]
 Arne Magnus, Certain continued fractions associated with the Podé table, Math. Z. 78 (1962), 361374. MR 27 #272. MR 0150271 (27:272)
 [8]
 , Expansion of power series into Pfractions, Math. Z. 80 (1962), 209216. MR 27 #273. MR 0150272 (27:273)
 [9]
 , On Pexpansions of power series, Norske Vid. Selsk. Skr. (Trondheim) 1964, no. 3, 14 pp. MR 32 #1330. MR 0183854 (32:1330)
 [10]
 , The connection between Pfractions and associated fractions, Proc. Amer. Math. Soc. 25 (1970), 676679. MR 41 #4050. MR 0259412 (41:4050)
 [11]
 W. T. Scott and H. S. Wall, Continued fraction expansions for arbitrary power series, Ann. of Math. (2) 41 (1940), 328349. MR 1, 296. MR 0001777 (1:296c)
 [12]
 V. Singh and W. J. Thron, On the number of singular points, located on the unit circle, of certain functions represented by Cfractions, Pacific J. Math. 6 (1956), 135143. MR 18, 274. MR 0080631 (18:274g)
 [13]
 W. J. Thron, Some properties of the continued fraction , Bull. Amer. Math. Soc 54 (1948), 206218. MR 9, 508. MR 0024528 (9:508c)
 [14]
 , Singular points of functions defined by Cfractions, Proc. Nat. Acad. Sci. U.S.A. 36 (1950), 5154, MR 11, 429. MR 0033363 (11:429c)
 [15]
 , A class of meromorphic functions having the unit circle as a natural boundary, Duke Math. J. 20 (1953), 195198. MR 15, 113. MR 0056691 (15:113e)
 [16]
 Haakon Waadeland, A convergence property of certain Tfraction expansions, Norske Vid. Selsk, Skr. (Trondheim) 1966, no. 9, 22 pp. MR 37 #1568. MR 0225978 (37:1568)
 [17]
 Haakon Waadeland, On Tfractions of certain functions with a first order pole at the point of infinity, Norske Vid. Selsk. Forh. (Trondheim) 40 (1967), 16. MR 38 #2289. MR 0233968 (38:2289)
 [18]
 , On Tfractions of functions holomorphic and bounded in a circular disc, Norske Vid. Selsk. Skr. (Trondheim) 1964, no. 8, 19 pp. MR 31 #1364. MR 0177100 (31:1364)
 [19]
 H. S. Wall, Analytic theory of continued fractions, Van Nostrand, Princeton, N.J., 1948. MR 10, 32. MR 0025596 (10:32d)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0002993919720291420X
PII:
S 00029939(1972)0291420X
Keywords:
Continued fraction,
Cfraction,
Tfraction,
Pfraction,
meromorphic function
Article copyright:
© Copyright 1972
American Mathematical Society
