Journal of Inequalities in Pure and
Applied Mathematics
http://jipam.vu.edu.au/
Volume 7, Issue 4, Article 156, 2006
ERRATA: INEQUALITIES ASSOCIATING HYPERGEOMETRIC FUNCTIONS
WITH PLANER HARMONIC MAPPINGS
OM P. AHUJA AND H. SILVERMAN
D EPARTMENT OF M ATHEMATICS
K ENT S TATE U NIVERSITY
B URTON , O HIO 44021-9500
oahuja@kent.edu
D EPARTMENT OF M ATHEMATICS
U NIVERSITY OF C HARLESTON
C HARLESTON , S OUTH C AROLINA 29424
silvermanh@cofc.edu
Received 13 April, 2006; accepted 04 August, 2006
Communicated by N.E. Cho
A BSTRACT. The purpose of this note is to give some corrections for our published article in [1].
Key words and phrases: Errata, Planar harmonic mappings, hypergeometric functions.
2000 Mathematics Subject Classification. 30C55, 31A05, 33C90.
These errata give the following correct statements for the corresponding statements on the
cited page of our published article [1].
Page 2
φ2 (z) := F (a2 , b2 ; c2 ; z) − 1 =
∞
X
(a2 )n (b2 )n
n=1
(c2 )n (1)n
zn,
|a2 b2 | < |c2 | .
Page 8 (After Remark 2.10: Line 4)
ψ2 (z) := ϕ(a2 , c2 ; z) − 1 =
∞
X
(a2 )n
n=1
ISSN (electronic): 1443-5756
c 2006 Victoria University. All rights reserved.
111-06
(c2 )n
zn,
|a2 | < |c2 | ,
2
O M P. A HUJA AND H. S ILVERMAN
Page 8 (After Remark 2.10: Line 9)
c1 − 1
and
c 1 − a1 − 1
a2
ψ2 (1) = F (a2 , 1; c2 ; 1) − 1 =
.
c 2 − a2 − 1
Page 8 (Theorem 2.20 : Last line)
ψ1 (1) = F (a1 , 1; c1 ; 1) =
(c1 − 1) (c1 − 2)
a22
+
≤ 2.
(c1 − a1 − 1) (c1 − a1 − 2) (c2 − a2 − 1) (c2 − a2 − 2)
Page 9 (Theorem 2.40 : Line 3)
c1 − 1
3a1
2a2
1+
+
(c1 − a1 − 1)
c1 − a1 − 2 (c1 − a1 − 3)2
a2
a2
2(a2 )2
+
+
≤ 2.
(c2 − a2 − 1) c2 − a2 − 2 (c2 − a2 − 3)2
Page 9 (Theorem 2.70 : Line 3)
a1
c2
+
≤ 1.
c 1 − a1 − 1 c 2 − a2 − 1
R EFERENCES
[1] OM P. AHUJA AND H. SILVERMAN, Inequalities associating hypergeometric functions with
planer harmonic mappings, J. Inequal. Pure Appl. Math., 5(4) (2004), Art. 99. [ONLINE: http:
//jipam.vu.edu.au/article.php?sid=454].
J. Inequal. Pure and Appl. Math., 7(4) Art. 156, 2006
http://jipam.vu.edu.au/