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Regarding solving a polynomial: gives empty output

Attachments:
Untitled-1.nb
POSTED BY: Neetasha Arya
6 Replies
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Ok, try with 3/2+1/5:

In[17]:= 
xxxx /. {me -> 1, Te -> 1, \[Omega]pe -> 1, \[Omega]ce -> 1, 
   ky -> 1, \[Epsilon]b -> 1, c -> 1, k -> 1, kpar -> 1, 
   kz -> 1, \[Omega]pi -> 1, 
   vde -> 1, \[Kappa] -> 3/2 + 1/5, \[Phi] -> Pi/6};
N[%*\[Omega]^2 // Simplify, 10] // Expand

Out[18]= -49.8649146 - 3491.27281 \[Omega] + 9421.90942 \[Omega]^2 + 
 643294.193 \[Omega]^3 - (42938.7191 + 141.5690054 I) \[Omega]^4 + 
 17009.04504 \[Omega]^6
POSTED BY: Gianluca Gorni

There is a limit for [kappa] value, it should be greater than 3/2.
POSTED BY: Neetasha Arya

Try with kappa=1/7:

xxx /. {me -> 1, Te -> 1, \[Omega]pe -> 1, \[Omega]ce -> 1, 
  ky -> 1, \[Epsilon]b -> 1, c -> 1, k -> 1, kpar -> 1, 
  kz -> 1, \[Omega]pi -> 1, 
  vde -> 1, \[Kappa] -> 1/7, \[Phi] -> Pi/6}
N[%*\[Omega]^2 // Simplify, 10] // Expand
POSTED BY: Gianluca Gorni

Even if I put the value of \Kappa = 2 (say), It is showing output as complex infinity.

.

Later If I evaluate it element wise, it is showing complex infinity for 

HypergeometricPFQ[{1/2, 1/2, 1}, {-\[Kappa] , 1, 1, 1}, 
 2*\[Lambda]*\[Kappa]]

and showing some answer for 

HypergeometricPFQ[{1, 1/2, 1}, {-\[Kappa] + 1/2, 1, 1, 1}, 
 2*\[Lambda]*\[Kappa]]

What is the problem ?

Attachments:
hypergeometic.nb
POSTED BY: Neetasha Arya

Your equation is of degree 6 in omega, with very complicated coefficients:

In[318]:= PolynomialQ[Expand[xxx*\[Omega]^2], \[Omega]]
Exponent[Expand[xxx*\[Omega]^2], \[Omega]]

Out[318]= True

Out[319]= 6

It seems hopless, unless you set most parameters to numbers.
POSTED BY: Gianluca Gorni
Eric Rimbey
Eric Rimbey
Posted 3 years ago

The empty lists means that Solve found no solutions. As for how to find solutions, your expressions are way too complicated for me to try to debug your code.
POSTED BY: Eric Rimbey
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