Landen inequalities for Gaussian hypergeometric function

• Published in: Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas Vol. 116; no. 1
• Main Authors: Zhao, Tie-Hong, Wang, Miao-Kun, Hai, Guo-Jing, Chu, Yu-Ming
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 2022; Springer Nature B.V
• Subjects: Applications of Mathematics; Hypergeometric functions; Inequalities; Mathematical and Computational Physics; Mathematics; Mathematics and Statistics; Original Paper; Theoretical; Landen inequalities; Ramanujan transformation; 33E05; Gaussian hypergeometric function; 33C05; Landen identity
• ISSN: 1578-7303; 1579-1505
• DOI: 10.1007/s13398-021-01197-y

In the article, we present several Landen inequalities, and quadratic and cubic transformation inequalities for general Gaussian hypergeometric function
2
F
1
(
a
,
b
;
c
;
x
)
. Our obtained results are the generalizations and improvements of the previously known results.