kencom1

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6 years, 245 days
UNIVERSITY OF LAGOS, AKOKA YABA, LAGOS
LAGOS, Nigeria

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These are questions asked by kencom1

Hello everyone, I was trying to plot graph for some functions but its just plotting one plot. Anyone with useful information please.

Pe.maple

theta := a-(1/2)*beta*a*y^2+(1/24)*beta^2*a*y^4-(1/720)*beta^3*a*y^6+(1/40320)*beta^4*a*y^8-(1/3628800)*beta^5*a*y^10+(1/479001600)*beta^6*a*y^12-(1/87178291200)*beta^7*a*y^14+(1/20922789888000)*beta^8*a*y^16-(1/6402373705728000)*beta^9*a*y^18+(1/2432902008176640000)*beta^10*a*y^20-(1/1124000727777607680000)*beta^11*a*y^22+(1/620448401733239439360000)*beta^12*a*y^24

Pls, anyone with useful informations on how to convert a series just like the one above to trigonometry or hyperbolic form. Need response as soon as possible. Thankin you in anticipation for your favorable response. 

Please Sir/Ma, I'm trying to generate a recurrent relations of this series and I try to use "if" "else" condition but I didn't get it right. Any one with useful suggestions. Appreciate 

 

restart;
Y[0] := A; Y[1] := B;
if k = a then delta(k-a) := 1 else 0 end if;
                               0
for k from 0 to 10 do Y[k+2] := solve(add(delta(i-1)*(k-i+1)*(k-i+2)*Y[k-i+2], i = 0 .. k)+add((delta(i)-delta(i-1))*(k-i+1)*Y[k-i+1], i = 0 .. k)+lambda*Y[k] = 0, Y[k+2]) end do;
y := sum(Y[j]*x^j, j = 0 .. 10);
 

Please, anybody with a good answer. Thanks in advance

restart;
U[0] := 1; U[1] := a; U[2] := 3/2; U[3] := (1/6)*b;
for k from 0 to 20 do U[k+4] := (4/factorial(k)+U[k])/((k+1)*(k+2)*(k+3)*(k+4)) end do;
u := sum(U[j]*y^j, j = 0 .. 20);
           3  2   1    3   5   4   /1     1   \  5    7   6
 1 + a y + - y  + - b y  + -- y  + |-- + --- a| y  + --- y 
           2      6        24      \30   120  /      720   

      / 1      1    \  7    1    8   /  1       1     \  9
    + |---- + ---- b| y  + ---- y  + |----- + ------ a| y 
      \1260   5040  /      4480      \45360   362880  /   

        11     10   /   1         1      \  11      13      12
    + ------- y   + |------- + -------- b| y   + --------- y  
      3628800       \4989600   39916800  /       479001600    

      /    1           1       \  13       1       14
    + |--------- + ---------- a| y   + ---------- y  
      \518918400   6227020800  /       5811886080    

      /     1               1        \  15         17        16
    + |------------ + ------------- b| y   + -------------- y  
      \108972864000   1307674368000  /       20922789888000    

      /      1                 1         \  17
    + |-------------- + --------------- a| y  
      \22230464256000   355687428096000  /    

             19         18
    + ---------------- y  
      6402373705728000    

      /       1                   1           \  19
    + |---------------- + ------------------ b| y  
      \7602818775552000   121645100408832000  /    

              1           20
    + ------------------ y  
      115852476579840000    
solve({(sum(U[j]*y^j, j = 0 .. 20), y = 1) = 2*exp(1), (sum(j*(j-1)*U[j]*y^j, j = 0 .. 20), y = 1) = 4*exp(1)}, [a, b]);
 

Download Sum_Sum.mw
 

Restart:

Digits := 10:

Ha := 2:

R := 2:

a := 0.1e-2:

Rt := 1:

Br := 1.5:

Xi := 0:

U[0] := 0:

U[1] := alpha:

U[2] := -6+(1/16)*Rt*Xi:

U[3] := (1/6)*beta:

T[0] := -(1/2)*Rt:

T[1] := phi:

``

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)

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)

``


 

Download Sum_Sum.mw

 

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