Simplify a symmetric complex function .
Lets consider the following symmetrical complex relation
$f(z) = frac{B(z)B(frac{1}{z})}{B(z)B(frac{1}{z}) + alpha A(z)A(frac{1}{z})}$
where $alpha$ is a real value, $B(z)=sum_{i=1}^{N}beta_i z^i$ and $A(z)=sum_{i=1}^{M}alpha_i z^i$. I am looking for a function $G(z)$ (as a function of $A$ and $B$) the satisfy the following relation
$f(z) = G(z)G(frac{1}{z})$
complex-analysis several-complex-variables
asked Nov 29 at 9:06
Arman
11
add a comment |
Lets consider the following symmetrical complex relation
$f(z) = frac{B(z)B(frac{1}{z})}{B(z)B(frac{1}{z}) + alpha A(z)A(frac{1}{z})}$
where $alpha$ is a real value, $B(z)=sum_{i=1}^{N}beta_i z^i$ and $A(z)=sum_{i=1}^{M}alpha_i z^i$. I am looking for a function $G(z)$ (as a function of $A$ and $B$) the satisfy the following relation
$f(z) = G(z)G(frac{1}{z})$
complex-analysis several-complex-variables
asked Nov 29 at 9:06
Arman
11
Welcome to MSE. Your question is phrased as an isolated problem, without any further information or context. This does not match many users' quality standards, so it may attract downvotes, or be put on hold. To prevent that, please edit the question. This will help you recognise and resolve the issues. Concretely: please provide context, and include your work and thoughts on the problem. These changes can help in formulating more appropriate answers.
– José Carlos Santos
Nov 29 at 9:11
I doubt it, since $$frac{1}{f(z)}=1+alphafrac{A(z)}{B(z)}frac{A(1/z)}{B(1/z)}$$
– MPW
Nov 29 at 9:52
add a comment |
Lets consider the following symmetrical complex relation
$f(z) = frac{B(z)B(frac{1}{z})}{B(z)B(frac{1}{z}) + alpha A(z)A(frac{1}{z})}$
where $alpha$ is a real value, $B(z)=sum_{i=1}^{N}beta_i z^i$ and $A(z)=sum_{i=1}^{M}alpha_i z^i$. I am looking for a function $G(z)$ (as a function of $A$ and $B$) the satisfy the following relation
$f(z) = G(z)G(frac{1}{z})$
complex-analysis several-complex-variables
asked Nov 29 at 9:06
Arman
11
Lets consider the following symmetrical complex relation
$f(z) = frac{B(z)B(frac{1}{z})}{B(z)B(frac{1}{z}) + alpha A(z)A(frac{1}{z})}$
where $alpha$ is a real value, $B(z)=sum_{i=1}^{N}beta_i z^i$ and $A(z)=sum_{i=1}^{M}alpha_i z^i$. I am looking for a function $G(z)$ (as a function of $A$ and $B$) the satisfy the following relation
$f(z) = G(z)G(frac{1}{z})$
complex-analysis several-complex-variables
complex-analysis several-complex-variables
asked Nov 29 at 9:06
Arman
11
asked Nov 29 at 9:06
Arman
11
edited Nov 30 at 8:35
asked Nov 29 at 9:06
Arman
11
asked Nov 29 at 9:06
Arman
11
asked Nov 29 at 9:06
Arman
11
11
Welcome to MSE. Your question is phrased as an isolated problem, without any further information or context. This does not match many users' quality standards, so it may attract downvotes, or be put on hold. To prevent that, please edit the question. This will help you recognise and resolve the issues. Concretely: please provide context, and include your work and thoughts on the problem. These changes can help in formulating more appropriate answers.
– José Carlos Santos
Nov 29 at 9:11
I doubt it, since $$frac{1}{f(z)}=1+alphafrac{A(z)}{B(z)}frac{A(1/z)}{B(1/z)}$$
– MPW
Nov 29 at 9:52
add a comment |
Welcome to MSE. Your question is phrased as an isolated problem, without any further information or context. This does not match many users' quality standards, so it may attract downvotes, or be put on hold. To prevent that, please edit the question. This will help you recognise and resolve the issues. Concretely: please provide context, and include your work and thoughts on the problem. These changes can help in formulating more appropriate answers.
– José Carlos Santos
Nov 29 at 9:11
I doubt it, since $$frac{1}{f(z)}=1+alphafrac{A(z)}{B(z)}frac{A(1/z)}{B(1/z)}$$
– MPW
Nov 29 at 9:52
Welcome to MSE. Your question is phrased as an isolated problem, without any further information or context. This does not match many users' quality standards, so it may attract downvotes, or be put on hold. To prevent that, please edit the question. This will help you recognise and resolve the issues. Concretely: please provide context, and include your work and thoughts on the problem. These changes can help in formulating more appropriate answers.
– José Carlos Santos
Nov 29 at 9:11
Welcome to MSE. Your question is phrased as an isolated problem, without any further information or context. This does not match many users' quality standards, so it may attract downvotes, or be put on hold. To prevent that, please edit the question. This will help you recognise and resolve the issues. Concretely: please provide context, and include your work and thoughts on the problem. These changes can help in formulating more appropriate answers.
– José Carlos Santos
Nov 29 at 9:11
I doubt it, since $$frac{1}{f(z)}=1+alphafrac{A(z)}{B(z)}frac{A(1/z)}{B(1/z)}$$
– MPW
Nov 29 at 9:52
I doubt it, since $$frac{1}{f(z)}=1+alphafrac{A(z)}{B(z)}frac{A(1/z)}{B(1/z)}$$
– MPW
Nov 29 at 9:52
add a comment |
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Welcome to MSE. Your question is phrased as an isolated problem, without any further information or context. This does not match many users' quality standards, so it may attract downvotes, or be put on hold. To prevent that, please edit the question. This will help you recognise and resolve the issues. Concretely: please provide context, and include your work and thoughts on the problem. These changes can help in formulating more appropriate answers.
– José Carlos Santos
Nov 29 at 9:11
I doubt it, since $$frac{1}{f(z)}=1+alphafrac{A(z)}{B(z)}frac{A(1/z)}{B(1/z)}$$
– MPW
Nov 29 at 9:52