fatemeh1090

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These are questions asked by fatemeh1090

HOW I CAN FIND A , B DIRECTLY?

NOT BY WRITING RELATION 5?

A.mw



Maple Worksheet - Error

Failed to load the worksheet /maplenet/convert/A.mw .
 

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Is there a similar function as (cylinderplot) to plot convex or concave toroidal shell segments?

This type of shell is as follows.

 

 

How I can plot3d function s. in the domain x ,y from -1300 to 200.

Thanks

if.mw
 

"restart;   #`    x__A`=-1300..200,      `y__A`=-1300..200    u1:=(((`x__A`-200)^(2)+(`y__A`^())^(2))*0.001)/(960000);   if  u1<=0.001  then w(u1):=-0.5772-ln(u1);  else if u1>0.001  then w(u1):=-0.5772-ln(u1)+u1-((u1)^(2))/(2*2!)+((u1)^(3))/(3*3!)-((u1)^(4))/(4*4!)+((u1)^(5))/(5*5!)-((u1)^(6))/(6*6!)+((u1)^(7))/(7*7!)-((u1)^(8))/(8*8!)+((u1)^(9))/(9*9!)-((u1)^(10))/(10*10!)+((u1)^(11))/(11*11!)-((u1)^(12))/(12*12!);     end if"

Error, invalid 'if' statement

"restart;      u1:=(((`x__A`-200)^2+(`y__A`)^2)*0.001)/960000;   if u1<=0.001  then w:=(u1)->-0.5772-ln(u1);  elseif u1>0.001  then w(u1):=-0.5772-ln(u1)+u1-((u1)^2)/(2*2!)+((u1)^3)/(3*3!)-((u1)^4)/(4*4!)+((u1)^5)/(5*5!)-((u1)^6)/(6*6!)+((u1)^7)/(7*7!)-((u1)^8)/(8*8!)+((u1)^9)/(9*9!)-((u1)^10)/(10*10!)+((u1)^11)/(11*11!)-((u1)^12)/(12*12!);     end if"

 

s := 6.87*10^(-3)*w(u1); plot3d(s, x__A = -1300 .. 200, y__A = -1300 .. 200)


 

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Hi everyone.

I have a 2D function and I wanna after Differentiating from it with respect to tau (at any amount of sigma value) and equaling this derivative to zero solve the infinite system of equations.

P[n](tau)==LegendreP(n - 1/2, cosh(tau)) , Q[n](tau)==LegendreQ(n - 1/2, cosh(tau)) 

are Legendre function.

Thanks in advanced

FUNCTION_f.mw


 

"restart;:N:=3: f(sigma,tau):=(sqrt(cosh(tau)-cos(sigma)))*(&sum;)(A[n]*P[n]((tau)) -n*Q[n]((tau)) )*sin(n*sigma)"

proc (sigma, tau) options operator, arrow, function_assign; sqrt(cosh(tau)-cos(sigma))*(sum((A[n]*P[n](tau)-n*Q[n](tau))*sin(n*sigma), n = 1 .. N)) end proc

(1)

NULL

W := simplify(diff(f(sigma, tau), tau))

(1/2)*((2*A[2]*(cosh(tau)-cos(sigma))*(diff(P[2](tau), tau))+(-4*cosh(tau)+4*cos(sigma))*(diff(Q[2](tau), tau))+sinh(tau)*(A[2]*P[2](tau)-2*Q[2](tau)))*sin(2*sigma)+(2*A[3]*(cosh(tau)-cos(sigma))*(diff(P[3](tau), tau))+(-6*cosh(tau)+6*cos(sigma))*(diff(Q[3](tau), tau))+sinh(tau)*(A[3]*P[3](tau)-3*Q[3](tau)))*sin(3*sigma)+sin(sigma)*(2*A[1]*(cosh(tau)-cos(sigma))*(diff(P[1](tau), tau))+(-2*cosh(tau)+2*cos(sigma))*(diff(Q[1](tau), tau))+sinh(tau)*(A[1]*P[1](tau)-Q[1](tau))))/(cosh(tau)-cos(sigma))^(1/2)

(2)

``


 

Download FUNCTION_f.mw

How I can prove the following equation in red box.

Also, Pn(v) and qn(v) are the real combinations of half-integer Legendre functions.

For more details please see 

https://math.stackexchange.com/questions/2746660/potential-flow-around-a-torus-laplace-equation-in-toroidal-coordinates/3809487#3809487

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