TY  - JOUR
AU  - András, Szilárd
AU  - Baricz, Árpád
TI  - Bounds for complete elliptic integrals of the first kind
JF  - EXPOSITIONES MATHEMATICAE
J2  - EXPO MATH
VL  - 28
PY  - 2010
IS  - 4
SP  - 357
EP  - 364
PG  - 8
SN  - 0723-0869
DO  - 10.1016/j.exmath.2009.12.005
UR  - https://m2.mtmt.hu/api/publication/1385763
ID  - 1385763
AB  - In this note by using some elementary computations we present some new sharp lower and upper bounds for the complete elliptic integrals of the first kind. These results improve some known bounds in the literature and are deduced from the well-known Wallis inequality, which has been studied extensively in the last 10 years.
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Baricz, Árpád
TI  - Convexity of the zero-balanced Gaussian hypergeometric functions with respect to Hölder means
JF  - JOURNAL OF INEQUALITIES IN PURE AND APPLIED MATHEMATICS
J2  - J INEQUAL PURE APPL MATH
VL  - 8
PY  - 2007
IS  - 2
SP  - 1
EP  - 9
PG  - 9
SN  - 1443-5756
UR  - https://m2.mtmt.hu/api/publication/1416258
ID  - 1416258
AB  - In this note we investigate the convexity of zero-balanced Gaussian hypergeometric functions and general power series with respect to Hölder means.
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Baricz, Árpád
TI  - Turán type inequalities for generalized complete elliptic integrals
JF  - MATHEMATISCHE ZEITSCHRIFT
J2  - MATH Z
VL  - 256
PY  - 2007
IS  - 4
SP  - 895
EP  - 911
PG  - 17
SN  - 0025-5874
DO  - 10.1007/s00209-007-0111-x
UR  - https://m2.mtmt.hu/api/publication/1353025
ID  - 1353025
AB  - In this paper our aim is to establish some Turán type inequalities for Gaussian hypergeometric functions and for generalized complete elliptic integrals. These results complete the earlier result of P. Turán proved for Legendre polynomials. Moreover we show that there is a close connection between a Turán type inequality and a sharp lower bound for the generalized complete elliptic integral of the first kind. At the end of this paper we prove a recent conjecture of T. Sugawa and M. Vuorinen related to estimates of the hyperbolic distance of the twice punctured plane.
LA  - English
DB  - MTMT
ER  -