A study of Horn matrix functions and Horn confluent matrix functions
Author:
Dwivedi Ravi1, Verma Ashish2
Affiliation:
1. Department of Science , SAGEMMC , Jagdalpur , Bastar, CG, 494001 , India 2. Department of Mathematics , Prof. Rajendra Singh (Rajju Bhaiya), Institute of Physical Sciences for Study and Research , 77032 V. B. S. Purvanchal University , Jaunpur (U.P.) 222003 , India
Abstract
Abstract
In this paper, we give the matrix version of Horn’s hypergeometric function and their confluent cases. We also discuss the regions of convergence, system of matrix differential equations of bilateral type, differential formulae and infinite summation formulae satisfied by these hypergeometric matrix functions. With the study of these 23 matrix functions, matrix generalization of Horn’s list of 34 hypergeometric series will be completed.
Publisher
Walter de Gruyter GmbH
Reference22 articles.
1. A. Altin, B. Çekim and R. Şahin,
On the matrix versions of Appell hypergeometric functions,
Quaest. Math. 37 (2014), no. 1, 31–38. 2. Y. A. Brychkov and N. V. Savischenko,
On some formulas for the Horn functions
G
1
(
a
,
b
,
b
;
w
,
z
)
G_{1}(a,b,b;w,z)
and
Γ
2
(
b
,
b
;
w
,
z
)
\Gamma_{2}(b,b;w,z)
,
Integral Transforms Spec. Funct. 31 (2020), no. 10, 804–819. 3. Y. A. Brychkov and N. V. Savischenko,
On some formulas for the Horn functions
G
2
(
a
,
a
,
b
,
b
;
w
,
z
)
G_{2}(a,a,b,b;w,z)
,
G
3
(
a
,
a
;
w
,
z
)
G_{3}(a,a;w,z)
and
Γ
1
(
a
,
b
,
b
;
w
,
z
)
\Gamma_{1}(a,b,b;w,z)
,
Integral Transforms Spec. Funct. 31 (2020), no. 11, 891–905. 4. Y. A. Brychkov and N. V. Savischenko,
On some formulas for the Horn functions
H
1
(
a
,
b
,
c
;
d
;
w
,
z
)
H_{1}(a,b,c;d;w,z)
and
H
1
(
c
)
(
a
,
b
;
d
;
w
,
z
)
H_{1}^{(c)}(a,b;d;w,z)
,
Integral Transforms Spec. Funct. 32 (2021), no. 1, 31–47. 5. Y. A. Brychkov and N. V. Savischenko,
On some formulas for the Horn functions
H
3
(
a
,
b
;
c
;
w
,
z
)
H_{3}(a,b;c;w,z)
,
H
6
(
c
)
(
a
;
c
;
w
,
z
)
H_{6}^{(c)}(a;c;w,z)
and Humbert function
ϕ
3
(
b
;
c
;
w
,
z
)
\phi_{3}(b;c;w,z)
,
Integral Transforms Spec. Funct. 32 (2021), no. 9, 661–676.
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