Asset Details
Do you wish to reserve the book?
A Malmquist–Steinmetz Theorem for Difference Equations
Hey, we have placed the reservation for you!
By the way, why not check out events that you can attend while you pick your title.
Oops! Something went wrong.
Looks like we were not able to place the reservation. Kindly try again later.
Are you sure you want to remove the book from the shelf?
A Malmquist–Steinmetz Theorem for Difference Equations
Do you wish to request the book?
A Malmquist–Steinmetz Theorem for Difference Equations
Please be aware that the book you have requested cannot be checked out. If you would like to checkout this book, you can reserve another copy
We have requested the book for you!
Your request is successful and it will be processed during the Library working hours. Please check the status of your request in My Requests.
Oops! Something went wrong.
Looks like we were not able to place your request. Kindly try again later.
Journal Article
A Malmquist–Steinmetz Theorem for Difference Equations
2024
Overview
It is shown that if the equation
f
(
z
+
1
)
n
=
R
(
z
,
f
)
,
where
R
(
z
,
f
) is rational in both arguments and
deg
f
(
R
(
z
,
f
)
)
≠
n
, has a transcendental meromorphic solution, then the equation above reduces into one out of several types of difference equations where the rational term
R
(
z
,
f
) takes particular forms. Solutions of these equations are presented in terms of Weierstrass or Jacobian elliptic functions, exponential type functions or functions which are solutions to a certain autonomous first-order difference equation having meromorphic solutions with preassigned asymptotic behavior. These results complement our previous work on the case
deg
f
(
R
(
z
,
f
)
)
=
n
of the equation above and thus provide a complete difference analogue of Steinmetz’ generalization of Malmquist’s theorem.
Publisher
Springer US,Springer Nature B.V
