Revisions to How can I plot this transcedental equation?

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edited Dec 29, 2017 at 20:04

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How can I plot $\kappa(\epsilon_{dd},\lambda)$ this transcendental equation? $$3\kappa \epsilon_{dd}\left[\left(\frac{\lambda^2}{2}+1\right)\frac{f_s(\kappa)}{1-\kappa^2}-1\right]+(\epsilon_{dd}-1)(\kappa^2-\lambda^2)=0 $$$$3\kappa^2 \epsilon_{dd}\left[\left(\frac{\lambda^2}{2}+1\right)\frac{f_s(\kappa)}{1-\kappa^2}-1\right]+(\epsilon_{dd}-1)(\kappa^2-\lambda^2)=0 $$ where $\lambda=1,2,3,4$ and $$f_s(\kappa)=\frac{1+2\kappa^2}{1-\kappa^2}-\frac{3\kappa^2 artanh \sqrt{1-\kappa^2} }{(1-\kappa^2)^{3/2}}. $$

My original problem is not that, but it's similar. If you help me with this, maybe I can solve mine.

Here are the codes of equations:

fs[kappa_] := (1 +3+2 kappa^2)/(1 - kappa^2) - (3 kappa^2 ArcTanh[
  Sqrt[1 - kappa^2]])/(1 - kappa^2)^(3/2)

3 kappakappa^2 edd (((lambda^2/2) + -1 ) fs[kappa]/(1 - kappa^2) - 
 1) + (edd - 1) (kappa^2 - lambda^2) == 0

How can I plot $\kappa(\epsilon_{dd},\lambda)$ this transcendental equation? $$3\kappa \epsilon_{dd}\left[\left(\frac{\lambda^2}{2}+1\right)\frac{f_s(\kappa)}{1-\kappa^2}-1\right]+(\epsilon_{dd}-1)(\kappa^2-\lambda^2)=0 $$ where $\lambda=1,2,3,4$ and $$f_s(\kappa)=\frac{1+2\kappa^2}{1-\kappa^2}-\frac{3\kappa^2 artanh \sqrt{1-\kappa^2} }{(1-\kappa^2)^{3/2}}. $$

My original problem is not that, but it's similar. If you help me with this, maybe I can solve mine.

Here are the codes of equations:

fs[kappa_] := (1 +3 kappa^2)/(1 - kappa^2) - (3 kappa^2 ArcTanh[
  Sqrt[1 - kappa^2]])/(1 - kappa^2)^(3/2)

3 kappa edd (((lambda^2/2) + 1) fs[kappa]/(1 - kappa^2) - 
 1) + (edd - 1) (kappa^2 - lambda^2) == 0

How can I plot $\kappa(\epsilon_{dd},\lambda)$ this transcendental equation? $$3\kappa^2 \epsilon_{dd}\left[\left(\frac{\lambda^2}{2}+1\right)\frac{f_s(\kappa)}{1-\kappa^2}-1\right]+(\epsilon_{dd}-1)(\kappa^2-\lambda^2)=0 $$ where $\lambda=1,2,3,4$ and $$f_s(\kappa)=\frac{1+2\kappa^2}{1-\kappa^2}-\frac{3\kappa^2 artanh \sqrt{1-\kappa^2} }{(1-\kappa^2)^{3/2}}. $$

My original problem is not that, but it's similar. If you help me with this, maybe I can solve mine.

Here are the codes of equations:

fs[kappa_] := (1 +2 kappa^2)/(1 - kappa^2) - (3 kappa^2 ArcTanh[
  Sqrt[1 - kappa^2]])/(1 - kappa^2)^(3/2)

3 kappa^2 edd (((lambda^2/2) -1 ) fs[kappa]/(1 - kappa^2) - 
 1) + (edd - 1) (kappa^2 - lambda^2) == 0

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edited Dec 29, 2017 at 17:04

Dinesh Shankar

375
1
10

How can I plot $\kappa(\epsilon_{dd},\lambda)$ this transcendental equation? $$3\kappa \epsilon_{dd}\left[\left(\frac{\lambda^2}{2}+1\right)\frac{f_s(\kappa)}{1-\kappa^2}-1\right]+(\epsilon_{dd}-1)(\kappa^2-\lambda^2)=0 $$ where $\lambda=1,2,3,4$ and $$f_s(\kappa)=\frac{1+3\kappa^2}{1-\kappa^2}-\frac{3\kappa^2 artanh \sqrt{1-\kappa^2} }{(1-\kappa^2)^{3/2}}. $$$$f_s(\kappa)=\frac{1+2\kappa^2}{1-\kappa^2}-\frac{3\kappa^2 artanh \sqrt{1-\kappa^2} }{(1-\kappa^2)^{3/2}}. $$

My original problem is not that, but it's similar. If you help me with this, maybe I can solve mine.

Here are the codes of equations:

fs[kappa_] := (1 +3 kappa^2)/(1 - kappa^2) - (3 kappa^2 ArcTanh[
  Sqrt[1 - kappa^2]])/(1 - kappa^2)^(3/2)

3 kappa edd (((lambda^2/2) + 1) fs[kappa]/(1 - kappa^2) - 
 1) + (edd - 1) (kappa^2 - lambda^2) == 0

How can I plot $\kappa(\epsilon_{dd},\lambda)$ this transcendental equation? $$3\kappa \epsilon_{dd}\left[\left(\frac{\lambda^2}{2}+1\right)\frac{f_s(\kappa)}{1-\kappa^2}-1\right]+(\epsilon_{dd}-1)(\kappa^2-\lambda^2)=0 $$ where $\lambda=1,2,3,4$ and $$f_s(\kappa)=\frac{1+3\kappa^2}{1-\kappa^2}-\frac{3\kappa^2 artanh \sqrt{1-\kappa^2} }{(1-\kappa^2)^{3/2}}. $$

My original problem is not that, but it's similar. If you help me with this, maybe I can solve mine.

Here are the codes of equations:

fs[kappa_] := (1 +3 kappa^2)/(1 - kappa^2) - (3 kappa^2 ArcTanh[
  Sqrt[1 - kappa^2]])/(1 - kappa^2)^(3/2)

3 kappa edd (((lambda^2/2) + 1) fs[kappa]/(1 - kappa^2) - 
 1) + (edd - 1) (kappa^2 - lambda^2) == 0

How can I plot $\kappa(\epsilon_{dd},\lambda)$ this transcendental equation? $$3\kappa \epsilon_{dd}\left[\left(\frac{\lambda^2}{2}+1\right)\frac{f_s(\kappa)}{1-\kappa^2}-1\right]+(\epsilon_{dd}-1)(\kappa^2-\lambda^2)=0 $$ where $\lambda=1,2,3,4$ and $$f_s(\kappa)=\frac{1+2\kappa^2}{1-\kappa^2}-\frac{3\kappa^2 artanh \sqrt{1-\kappa^2} }{(1-\kappa^2)^{3/2}}. $$

My original problem is not that, but it's similar. If you help me with this, maybe I can solve mine.

Here are the codes of equations:

fs[kappa_] := (1 +3 kappa^2)/(1 - kappa^2) - (3 kappa^2 ArcTanh[
  Sqrt[1 - kappa^2]])/(1 - kappa^2)^(3/2)

3 kappa edd (((lambda^2/2) + 1) fs[kappa]/(1 - kappa^2) - 
 1) + (edd - 1) (kappa^2 - lambda^2) == 0

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edited Dec 29, 2017 at 14:11

Dinesh Shankar

375
1
10

How can I plot $\kappa(\epsilon_{dd},\lambda)$ this transcendental equation? $$3\kappa \epsilon_{dd}\left[\left(\frac{\lambda^2}{2}+1\right)\frac{f_s(\kappa)}{1-\kappa^2}-1\right]+(\epsilon_{dd}-1)(\kappa^2-\lambda^2)=0 $$ where $\lambda=1,2,3,4$ and $$f_s(\kappa)=\frac{1+3\kappa^2}{1-\kappa^2}-\frac{3\kappa^2 artanh \sqrt{1-\kappa^2} }{(1-\kappa^2)^{3/2}}. $$

My original problem is not that, but it's similar. If you help me with this, maybe I can solve mine.

Here are the codes of equations:

fs[kappa_] := (1 +3 kappa^2)/(1 - kappa^2) - (3 kappa^2 ArcTanh[
  Sqrt[1 - kappa^2]])/(1 - kappa^2)^(3/2)

3 kappa edd5edd (((lambda^2/2) + 1) fs[kappa]/(1 - kappa^2) - 
 1) + (edd - 1) (kappa^2 - lambda^2) == 0

How can I plot $\kappa(\epsilon_{dd},\lambda)$ this transcendental equation? $$3\kappa \epsilon_{dd}\left[\left(\frac{\lambda^2}{2}+1\right)\frac{f_s(\kappa)}{1-\kappa^2}-1\right]+(\epsilon_{dd}-1)(\kappa^2-\lambda^2)=0 $$ where $\lambda=1,2,3,4$ and $$f_s(\kappa)=\frac{1+3\kappa^2}{1-\kappa^2}-\frac{3\kappa^2 artanh \sqrt{1-\kappa^2} }{(1-\kappa^2)^{3/2}}. $$

My original problem is not that, but it's similar. If you help me with this, maybe I can solve mine.

Here are the codes of equations:

fs[kappa_] := (1 +3 kappa^2)/(1 - kappa^2) - (3 kappa^2 ArcTanh[
  Sqrt[1 - kappa^2]])/(1 - kappa^2)^(3/2)

3 kappa edd5 (((lambda^2/2) + 1) fs[kappa]/(1 - kappa^2) - 
 1) + (edd - 1) (kappa^2 - lambda^2) == 0

How can I plot $\kappa(\epsilon_{dd},\lambda)$ this transcendental equation? $$3\kappa \epsilon_{dd}\left[\left(\frac{\lambda^2}{2}+1\right)\frac{f_s(\kappa)}{1-\kappa^2}-1\right]+(\epsilon_{dd}-1)(\kappa^2-\lambda^2)=0 $$ where $\lambda=1,2,3,4$ and $$f_s(\kappa)=\frac{1+3\kappa^2}{1-\kappa^2}-\frac{3\kappa^2 artanh \sqrt{1-\kappa^2} }{(1-\kappa^2)^{3/2}}. $$

My original problem is not that, but it's similar. If you help me with this, maybe I can solve mine.

Here are the codes of equations:

fs[kappa_] := (1 +3 kappa^2)/(1 - kappa^2) - (3 kappa^2 ArcTanh[
  Sqrt[1 - kappa^2]])/(1 - kappa^2)^(3/2)

3 kappa edd (((lambda^2/2) + 1) fs[kappa]/(1 - kappa^2) - 
 1) + (edd - 1) (kappa^2 - lambda^2) == 0

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edited Dec 29, 2017 at 14:02

Dinesh Shankar

375
1
10

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edited Dec 29, 2017 at 13:53

Dinesh Shankar

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edited Dec 29, 2017 at 12:36

Dinesh Shankar

375
1
10

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edited Dec 29, 2017 at 12:31

Dinesh Shankar

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asked Dec 29, 2017 at 11:55

Dinesh Shankar

375
1
10

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