Expressing a function in terms of another

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I know this is a very nonsense question. But, it has become challenging for me to visualize. I have two functions as seen following:

$$rho=sum_jin Jfraclambda_jmu_j$$
and
$$theta=sum_jin Jfraclambda_jmu_j^2$$

Is there any way to express $theta$ in terms of $rho$ or vice versa?

functional-analysis

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edited Jul 25 at 16:38

asked Jul 25 at 16:14

user8028576

277

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  I would say, "No." How would you express $frac1a+frac1b$ in terms of $frac1a^2+frac1b^2?$
  – saulspatz
  Jul 25 at 16:18
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  I also said, "No" and that's why I wanted to get more opinions. On the other hand, it seems, I can write $theta = sum_jin Jfraclambda_jmu_jfrac1mu_j stackrel?= frac1mu_jsum_jin Jfraclambda_jmu_j$. Then, what is gonna happen with $frac1mu_j$?
  – user8028576
  Jul 25 at 16:24
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  You can't pull $1/u_j$ out of the summation sign. Its value is different in every term of the sum.
  – saulspatz
  Jul 25 at 16:28
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @saulspatz, I am well aware of that. Just trying to put here something to get help if there is any possible way of doing that.
  – user8028576
  Jul 25 at 16:30
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  My best attempt: $$theta= - sum_j in J fracpartialpartial mu_j rho$$ but it's really not easier than just writing $$theta = sum_j in J fraclambda_jmu_j^2.$$
  – md2perpe
  Jul 25 at 18:29
  
  

  
  
  
  

add a comment | 

up vote
0
down vote

favorite

I know this is a very nonsense question. But, it has become challenging for me to visualize. I have two functions as seen following:

$$rho=sum_jin Jfraclambda_jmu_j$$
and
$$theta=sum_jin Jfraclambda_jmu_j^2$$

Is there any way to express $theta$ in terms of $rho$ or vice versa?

functional-analysis

share|cite|improve this question

edited Jul 25 at 16:38

asked Jul 25 at 16:14

user8028576

277

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  I would say, "No." How would you express $frac1a+frac1b$ in terms of $frac1a^2+frac1b^2?$
  – saulspatz
  Jul 25 at 16:18
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  I also said, "No" and that's why I wanted to get more opinions. On the other hand, it seems, I can write $theta = sum_jin Jfraclambda_jmu_jfrac1mu_j stackrel?= frac1mu_jsum_jin Jfraclambda_jmu_j$. Then, what is gonna happen with $frac1mu_j$?
  – user8028576
  Jul 25 at 16:24
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  You can't pull $1/u_j$ out of the summation sign. Its value is different in every term of the sum.
  – saulspatz
  Jul 25 at 16:28
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @saulspatz, I am well aware of that. Just trying to put here something to get help if there is any possible way of doing that.
  – user8028576
  Jul 25 at 16:30
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  My best attempt: $$theta= - sum_j in J fracpartialpartial mu_j rho$$ but it's really not easier than just writing $$theta = sum_j in J fraclambda_jmu_j^2.$$
  – md2perpe
  Jul 25 at 18:29
  
  

  
  
  
  

add a comment | 

up vote
0
down vote

favorite

up vote
0
down vote

favorite

I know this is a very nonsense question. But, it has become challenging for me to visualize. I have two functions as seen following:

$$rho=sum_jin Jfraclambda_jmu_j$$
and
$$theta=sum_jin Jfraclambda_jmu_j^2$$

Is there any way to express $theta$ in terms of $rho$ or vice versa?

functional-analysis

share|cite|improve this question

edited Jul 25 at 16:38

asked Jul 25 at 16:14

user8028576

277

I know this is a very nonsense question. But, it has become challenging for me to visualize. I have two functions as seen following:

$$rho=sum_jin Jfraclambda_jmu_j$$
and
$$theta=sum_jin Jfraclambda_jmu_j^2$$

Is there any way to express $theta$ in terms of $rho$ or vice versa?

functional-analysis

share|cite|improve this question

edited Jul 25 at 16:38

asked Jul 25 at 16:14

user8028576

277

share|cite|improve this question

share|cite|improve this question

edited Jul 25 at 16:38

edited Jul 25 at 16:38

edited Jul 25 at 16:38

asked Jul 25 at 16:14

user8028576

277

asked Jul 25 at 16:14

user8028576

277

asked Jul 25 at 16:14

user8028576

277

277

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  I would say, "No." How would you express $frac1a+frac1b$ in terms of $frac1a^2+frac1b^2?$
  – saulspatz
  Jul 25 at 16:18
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  I also said, "No" and that's why I wanted to get more opinions. On the other hand, it seems, I can write $theta = sum_jin Jfraclambda_jmu_jfrac1mu_j stackrel?= frac1mu_jsum_jin Jfraclambda_jmu_j$. Then, what is gonna happen with $frac1mu_j$?
  – user8028576
  Jul 25 at 16:24
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  You can't pull $1/u_j$ out of the summation sign. Its value is different in every term of the sum.
  – saulspatz
  Jul 25 at 16:28
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @saulspatz, I am well aware of that. Just trying to put here something to get help if there is any possible way of doing that.
  – user8028576
  Jul 25 at 16:30
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  My best attempt: $$theta= - sum_j in J fracpartialpartial mu_j rho$$ but it's really not easier than just writing $$theta = sum_j in J fraclambda_jmu_j^2.$$
  – md2perpe
  Jul 25 at 18:29
  
  

  
  
  
  

add a comment | 

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  I would say, "No." How would you express $frac1a+frac1b$ in terms of $frac1a^2+frac1b^2?$
  – saulspatz
  Jul 25 at 16:18
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  I also said, "No" and that's why I wanted to get more opinions. On the other hand, it seems, I can write $theta = sum_jin Jfraclambda_jmu_jfrac1mu_j stackrel?= frac1mu_jsum_jin Jfraclambda_jmu_j$. Then, what is gonna happen with $frac1mu_j$?
  – user8028576
  Jul 25 at 16:24
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  You can't pull $1/u_j$ out of the summation sign. Its value is different in every term of the sum.
  – saulspatz
  Jul 25 at 16:28
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @saulspatz, I am well aware of that. Just trying to put here something to get help if there is any possible way of doing that.
  – user8028576
  Jul 25 at 16:30
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  My best attempt: $$theta= - sum_j in J fracpartialpartial mu_j rho$$ but it's really not easier than just writing $$theta = sum_j in J fraclambda_jmu_j^2.$$
  – md2perpe
  Jul 25 at 18:29
  
  

  
  
  
  

1

1

I would say, "No." How would you express $frac1a+frac1b$ in terms of $frac1a^2+frac1b^2?$
– saulspatz
Jul 25 at 16:18

I would say, "No." How would you express $frac1a+frac1b$ in terms of $frac1a^2+frac1b^2?$
– saulspatz
Jul 25 at 16:18

I also said, "No" and that's why I wanted to get more opinions. On the other hand, it seems, I can write $theta = sum_jin Jfraclambda_jmu_jfrac1mu_j stackrel?= frac1mu_jsum_jin Jfraclambda_jmu_j$. Then, what is gonna happen with $frac1mu_j$?
– user8028576
Jul 25 at 16:24

I also said, "No" and that's why I wanted to get more opinions. On the other hand, it seems, I can write $theta = sum_jin Jfraclambda_jmu_jfrac1mu_j stackrel?= frac1mu_jsum_jin Jfraclambda_jmu_j$. Then, what is gonna happen with $frac1mu_j$?
– user8028576
Jul 25 at 16:24

You can't pull $1/u_j$ out of the summation sign. Its value is different in every term of the sum.
– saulspatz
Jul 25 at 16:28

You can't pull $1/u_j$ out of the summation sign. Its value is different in every term of the sum.
– saulspatz
Jul 25 at 16:28

@saulspatz, I am well aware of that. Just trying to put here something to get help if there is any possible way of doing that.
– user8028576
Jul 25 at 16:30

@saulspatz, I am well aware of that. Just trying to put here something to get help if there is any possible way of doing that.
– user8028576
Jul 25 at 16:30

My best attempt: $$theta= - sum_j in J fracpartialpartial mu_j rho$$ but it's really not easier than just writing $$theta = sum_j in J fraclambda_jmu_j^2.$$
– md2perpe
Jul 25 at 18:29

My best attempt: $$theta= - sum_j in J fracpartialpartial mu_j rho$$ but it's really not easier than just writing $$theta = sum_j in J fraclambda_jmu_j^2.$$
– md2perpe
Jul 25 at 18:29

add a comment | 

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