Abstract
The incomplete gamma function Γ(a, u) is defined by
Γ
(
a
,
u
)
=
∫
u
∞
t
a
−
1
e
−
t
d
t
,
$$\Gamma(a,u)=\int\limits_{u}^{\infty}t^{a-1}\textrm{e}^{-t}\textrm{d} t,$$
where u > 0. Using the incomplete gamma function, we define a new Poisson like regular matrix
P
(
μ
)
=
(
p
n
k
μ
)
$\mathfrak{P}(\mu)=(p^{\mu}_{nk})$
given by
p
n
k
μ
=
n
!
Γ
(
n
+
1
,
μ
)
e
−
μ
μ
k
k
!
(
0
≤
k
≤
n
)
,
0
(
k
>
n
)
,
$$p^{\mu}_{nk}= \begin{cases} \dfrac{n!}{\Gamma(n+1,\mu)}\dfrac{\textrm{e}^{-\mu}\mu^k}{k!} \quad &(0\leq k\leq n), \\[1ex] 0\quad & (k>n), \end{cases}$$
where μ > 0 is fixed. We introduce the sequence space
ℓ
p
(
P
(
μ
)
)
$\ell_p(\mathfrak{P}(\mu))$
for 1 ≤ p ≤ ∞ and some topological properties, inclusion relations and generalized duals of the newly defined space are discussed. Also we characterize certain matrix classes and compact operators related to the space
ℓ
p
(
P
(
μ
)
)
$\ell_p(\mathfrak{P}(\mu))$
. We obtain Gurarii’s modulus of convexity and investigate some geometric properties of the new space. Finally, spectrum of the operator
P
(
μ
)
$\mathfrak{P}(\mu)$
on sequence space c
0 has been investigated.
Analytical Approximation Algorithm for the Inverse of the Power of the Incomplete Gamma Function Based on Extreme Value Theory
