Mixing
Inverse of a function with summation
Suppose that I have the following function:
$$z(zeta)=sum_{k=0}^{n}m_kzeta^{1-k}$$
How do I get the inverse of that function? i.e. I want to express $zeta(z)$?
In my case, $10leq n leq 20$.
In my case, $z$ cannot be zero and the constants $m_k$ is not arbitrary but rather obtained from another process. This is actually a conformal mapping function that can map any shape into a unit circle, thus $z$ cannot be zero.
Is it possible to have a general rule to defined $zeta(z)$? I can then translate them into Matlab, for instance.
inverse-function
asked Nov 9 '18 at 21:11
BeeTiau
568
add a comment |
Suppose that I have the following function:
$$z(zeta)=sum_{k=0}^{n}m_kzeta^{1-k}$$
How do I get the inverse of that function? i.e. I want to express $zeta(z)$?
In my case, $10leq n leq 20$.
In my case, $z$ cannot be zero and the constants $m_k$ is not arbitrary but rather obtained from another process. This is actually a conformal mapping function that can map any shape into a unit circle, thus $z$ cannot be zero.
Is it possible to have a general rule to defined $zeta(z)$? I can then translate them into Matlab, for instance.
inverse-function
asked Nov 9 '18 at 21:11
BeeTiau
568
nobody is interested to reply to my question? :)
– BeeTiau
Nov 13 '18 at 18:02
add a comment |
Suppose that I have the following function:
$$z(zeta)=sum_{k=0}^{n}m_kzeta^{1-k}$$
How do I get the inverse of that function? i.e. I want to express $zeta(z)$?
In my case, $10leq n leq 20$.
In my case, $z$ cannot be zero and the constants $m_k$ is not arbitrary but rather obtained from another process. This is actually a conformal mapping function that can map any shape into a unit circle, thus $z$ cannot be zero.
Is it possible to have a general rule to defined $zeta(z)$? I can then translate them into Matlab, for instance.
inverse-function
asked Nov 9 '18 at 21:11
BeeTiau
568
Suppose that I have the following function:
$$z(zeta)=sum_{k=0}^{n}m_kzeta^{1-k}$$
How do I get the inverse of that function? i.e. I want to express $zeta(z)$?
In my case, $10leq n leq 20$.
In my case, $z$ cannot be zero and the constants $m_k$ is not arbitrary but rather obtained from another process. This is actually a conformal mapping function that can map any shape into a unit circle, thus $z$ cannot be zero.
Is it possible to have a general rule to defined $zeta(z)$? I can then translate them into Matlab, for instance.
inverse-function
inverse-function
asked Nov 9 '18 at 21:11
BeeTiau
568
asked Nov 9 '18 at 21:11
BeeTiau
568
edited Nov 20 '18 at 12:43
asked Nov 9 '18 at 21:11
BeeTiau
568
asked Nov 9 '18 at 21:11
BeeTiau
568
asked Nov 9 '18 at 21:11
BeeTiau
568
568
nobody is interested to reply to my question? :)
– BeeTiau
Nov 13 '18 at 18:02
add a comment |
nobody is interested to reply to my question? :)
– BeeTiau
Nov 13 '18 at 18:02
nobody is interested to reply to my question? :)
– BeeTiau
Nov 13 '18 at 18:02
nobody is interested to reply to my question? :)
– BeeTiau
Nov 13 '18 at 18:02
add a comment |
1 Answer
1
active
oldest
votes
In general your function will not have an inverse function.
Consider for example
$$z(zeta):=zeta-3+frac{2}{zeta}$$
which has the property
$$z(1)=z(2)=0.$$
Thus, it's not one-to-one and you can't define an inverse function on the whole range of $z$.
answered Nov 14 '18 at 9:30
weee
4608
In my case, $z$ cannot be zero and the constants $m_k$ is not arbitrary but rather obtained from another process. This is actually a conformal mapping function that can map any shape into a unit circle, thus $z$ cannot be zero.
– BeeTiau
Nov 15 '18 at 16:19
Then you should add these additional condition to your question!
– weee
Nov 20 '18 at 9:05
Done. I have added the condition into my question. ^_^
– BeeTiau
Nov 20 '18 at 12:44
add a comment |
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1 Answer
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active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
In general your function will not have an inverse function.
Consider for example
$$z(zeta):=zeta-3+frac{2}{zeta}$$
which has the property
$$z(1)=z(2)=0.$$
Thus, it's not one-to-one and you can't define an inverse function on the whole range of $z$.
answered Nov 14 '18 at 9:30
weee
4608
In my case, $z$ cannot be zero and the constants $m_k$ is not arbitrary but rather obtained from another process. This is actually a conformal mapping function that can map any shape into a unit circle, thus $z$ cannot be zero.
– BeeTiau
Nov 15 '18 at 16:19
Then you should add these additional condition to your question!
– weee
Nov 20 '18 at 9:05
Done. I have added the condition into my question. ^_^
– BeeTiau
Nov 20 '18 at 12:44
add a comment |
In general your function will not have an inverse function.
Consider for example
$$z(zeta):=zeta-3+frac{2}{zeta}$$
which has the property
$$z(1)=z(2)=0.$$
Thus, it's not one-to-one and you can't define an inverse function on the whole range of $z$.
answered Nov 14 '18 at 9:30
weee
4608
In my case, $z$ cannot be zero and the constants $m_k$ is not arbitrary but rather obtained from another process. This is actually a conformal mapping function that can map any shape into a unit circle, thus $z$ cannot be zero.
– BeeTiau
Nov 15 '18 at 16:19
Then you should add these additional condition to your question!
– weee
Nov 20 '18 at 9:05
Done. I have added the condition into my question. ^_^
– BeeTiau
Nov 20 '18 at 12:44
add a comment |
In general your function will not have an inverse function.
Consider for example
$$z(zeta):=zeta-3+frac{2}{zeta}$$
which has the property
$$z(1)=z(2)=0.$$
Thus, it's not one-to-one and you can't define an inverse function on the whole range of $z$.
answered Nov 14 '18 at 9:30
weee
4608
In general your function will not have an inverse function.
Consider for example
$$z(zeta):=zeta-3+frac{2}{zeta}$$
which has the property
$$z(1)=z(2)=0.$$
Thus, it's not one-to-one and you can't define an inverse function on the whole range of $z$.
answered Nov 14 '18 at 9:30
weee
4608
answered Nov 14 '18 at 9:30
weee
4608
answered Nov 14 '18 at 9:30
weee
4608
answered Nov 14 '18 at 9:30
weee
4608
4608
In my case, $z$ cannot be zero and the constants $m_k$ is not arbitrary but rather obtained from another process. This is actually a conformal mapping function that can map any shape into a unit circle, thus $z$ cannot be zero.
– BeeTiau
Nov 15 '18 at 16:19
Then you should add these additional condition to your question!
– weee
Nov 20 '18 at 9:05
Done. I have added the condition into my question. ^_^
– BeeTiau
Nov 20 '18 at 12:44
add a comment |
In my case, $z$ cannot be zero and the constants $m_k$ is not arbitrary but rather obtained from another process. This is actually a conformal mapping function that can map any shape into a unit circle, thus $z$ cannot be zero.
– BeeTiau
Nov 15 '18 at 16:19
Then you should add these additional condition to your question!
– weee
Nov 20 '18 at 9:05
Done. I have added the condition into my question. ^_^
– BeeTiau
Nov 20 '18 at 12:44
In my case, $z$ cannot be zero and the constants $m_k$ is not arbitrary but rather obtained from another process. This is actually a conformal mapping function that can map any shape into a unit circle, thus $z$ cannot be zero.
– BeeTiau
Nov 15 '18 at 16:19
In my case, $z$ cannot be zero and the constants $m_k$ is not arbitrary but rather obtained from another process. This is actually a conformal mapping function that can map any shape into a unit circle, thus $z$ cannot be zero.
– BeeTiau
Nov 15 '18 at 16:19
Then you should add these additional condition to your question!
– weee
Nov 20 '18 at 9:05
Then you should add these additional condition to your question!
– weee
Nov 20 '18 at 9:05
Done. I have added the condition into my question. ^_^
– BeeTiau
Nov 20 '18 at 12:44
Done. I have added the condition into my question. ^_^
– BeeTiau
Nov 20 '18 at 12:44
add a comment |
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nobody is interested to reply to my question? :)
– BeeTiau
Nov 13 '18 at 18:02