Abstract
AbstractHahn’s difference operator $D_{q;w}f(x) =({f(qx+w)-f(x)})/({(q-1)x+w})$
D
q
;
w
f
(
x
)
=
(
f
(
q
x
+
w
)
−
f
(
x
)
)
/
(
(
q
−
1
)
x
+
w
)
, $q\in (0,1)$
q
∈
(
0
,
1
)
, $w>0$
w
>
0
, $x\neq w/(1-q)$
x
≠
w
/
(
1
−
q
)
is used to unify the recently established difference and q-asymptotic iteration methods (DAIM, qAIM). The technique is applied to solve the second-order linear Hahn difference equations. The necessary and sufficient conditions for polynomial solutions are derived and examined for the $(q;w)$
(
q
;
w
)
-hypergeometric equation.
Funder
Canadian Network for Research and Innovation in Machining Technology, Natural Sciences and Engineering Research Council of Canada
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Algebra and Number Theory,Analysis
Cited by
1 articles.
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