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Question: Need to generate the series for T[i] as it was generated for U[i]

Question:Need to generate the series for T[i] as it was generated for U[i]

kencom1 110 Maple
series
November 22 2016
0

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> 

Restart:
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Digits := 10:
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Ha := 2:
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R := 2:
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a := 0.1e-2:
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Rt := 1:
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Br := 1.5:
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Xi := 0:
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U[0] := 0:
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U[1] := alpha:
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U[2] := -6+(1/16)*Rt*Xi:
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U[3] := (1/6)*beta:
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T[0] := -(1/2)*Rt:
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T[1] := phi:
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``
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delta := proc (k) options operator, arrow; `if`(k = 0, 1, 0) end proc;

proc (k) options operator, arrow; `if`(k = 0, 1, 0) end proc

 (1)
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for k from 0 to 10 do U[k+4] := ((Ha^2+R)*U[k+2]+Xi*T[k+2])/((4*(k+3))*(k+4)); sum((1+(4/3)*R+4*a*R*T[i])*(k-i+1)*(k-i+2)*T[k-i+2], i = 0 .. k) := -4*a*R*(sum((i+1)*T[i+1]*(k-i+1)*T[k-i+1], i = 0 .. k))-Br*(sum((i+1)*U[i+1]*(k-i+1)*U[k-i+1], i = 0 .. k))+(1/4)*Ha^2*Br*(sum(U[i]*U[k-i], i = 0 .. k)) end do:
> 

u := sum(U[j]*y^j, j = 0 .. 9)

alpha*y-6*y^2+(1/6)*beta*y^3-(3/4)*y^4+(1/80)*beta*y^5-(3/80)*y^6+(1/2240)*beta*y^7-(9/8960)*y^8+(1/107520)*beta*y^9

 (2)
> 

``


 

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