On the Convexity and Concavity of Generalized Complete Elliptic Integral of the First Kind
In this paper, we study the convexity (concavity) of the function x ↦ K a ( x ) - log 1 + c / 1 - x on (0, 1) for a ∈ ( 0 , 1 / 2 ] and c ∈ ( 0 , ∞ ) , where K a ( r ) is the generalized complete elliptic integral of the first kind. This work is an extension of Yang and Tian (Appl Anal Discrete Math...
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| Veröffentlicht in: | Resultate der Mathematik 2022-12, Vol.77 (6), Article 215 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | In this paper, we study the convexity (concavity) of the function
x
↦
K
a
(
x
)
-
log
1
+
c
/
1
-
x
on (0, 1) for
a
∈
(
0
,
1
/
2
]
and
c
∈
(
0
,
∞
)
, where
K
a
(
r
)
is the generalized complete elliptic integral of the first kind. This work is an extension of Yang and Tian (Appl Anal Discrete Math 13:240–260, 2019), and also gives a refinement of inequality (Yang and Tian 2019, 0.27) as an application. |
|---|---|
| ISSN: | 1422-6383 1420-9012 |
| DOI: | 10.1007/s00025-022-01755-9 |