## 235 Reputation

10 years, 318 days
Beijing, China

## Define axis for 2D plotting ...

Maple 2015

Dear users! I want to define y-axes like Re^(1/2)*C[f] in the following expression

restart; plot([sin, cos], -Pi .. Pi, title = "Simple Trig Functions", legend = ["Sine Plot", "Cosine Plot"], titlefont = ["ARIAL", 15], labels = ["x values", typeset("Re", C__f)], labeldirections = ["horizontal", "vertical"], labelfont = ["HELVETICA", 16], linestyle = [solid, longdash], axesfont = ["HELVETICA", "ROMAN", 16], legendstyle = [font = ["HELVETICA", 9], location = right], tickmarks = [[-Pi = -180^o, -2*Pi*(1/3) = -120^o, -(1/3)*Pi = -60^o, 0 = `0`^o, (1/3)*Pi = 60^o, 2*Pi*(1/3) = 120^o, Pi = 180^o], default]);

## Problem in summation...

Maple 2015

Dear Users!

Hope you would be fine with everything. The following expression doesn't work for M=4,N=2,alpha=1. Please see the problem and try to fix. I shall be very thankful.

simplify(sum(sum(((-1)^i2*GAMMA(N-i2+alpha)*2^(N-2*i2)/(GAMMA(alpha)*factorial(i2)*factorial(N-2*i2)*(N-2*i2+1))*(GAMMA(k+1)*(k+alpha)*GAMMA(alpha)^2/(Pi*2^(1-2*alpha)*GAMMA(k+2*alpha))))*(sum((1/2)*(-1)^i*GAMMA(k-i+alpha)*2^(k-2*i)*(1+(-1)^(N-2*i2+1+k-2*i))*GAMMA((1/2)*N-i2+1+(1/2)*k-i)*GAMMA(alpha+1/2)*L[k]/(GAMMA(alpha)*factorial(i)*factorial(k-2*i)*GAMMA(alpha+3/2+(1/2)*N-i2+(1/2)*k-i)), i = 0 .. floor((1/2)*k))), i2 = 0 .. floor((1/2)*N)), k = 0 .. M))

## Simplification of an expression...

Maple 2015

Dear users!

Hope everyone should be fine here. I need the following simiplification. I did it step by step is there and maple command to do this.

(diff(theta(eta), eta, eta))*(Rd*T[infinity]^3*(`&theta;w`-1)^3*theta(eta)^3+3*Rd*T[infinity]^3*(`&theta;w`-1)^2*theta(eta)^2+(3*(Rd*T[infinity]^3+(1/3)*epsilon*k[nf]))*(`&theta;w`-1)*theta(eta)+Rd*T[infinity]^3+k[nf]) = (-3*Rd*T[infinity]^3*(`&theta;w`-1)^3*theta(eta)^2-6*Rd*T[infinity]^3*(`&theta;w`-1)^2*theta(eta)+(-3*Rd*T[infinity]^3-epsilon*k[nf])*(`&theta;w`-1))*(diff(theta(eta), eta))^2+(-(rho*c[p])[nf]*nu[f]*f(eta)-(rho*c[p])[nf]*nu[f]*g(eta))*(diff(theta(eta), eta))+a*nu[f]*mu[nf]*(diff(f(eta), eta))^2/((-`&theta;w`+1)*T[infinity])-2*a*nu[f]*mu[nf]*(diff(g(eta), eta))*(diff(f(eta), eta))/((`&theta;w`-1)*T[infinity])+a*nu[f]*mu[nf]*(diff(g(eta), eta))^2/((-`&theta;w`+1)*T[infinity])

(diff(theta(eta), eta, eta))*Rd*T[infinity]^3*(theta(eta)*`&theta;w`-theta(eta)+1)^3+(diff(theta(eta), eta, eta))*k[nf]*(epsilon*theta(eta)*`&theta;w`-epsilon*theta(eta)+1)+3*Rd*T[infinity]^3*(`&theta;w`-1)*(theta(eta)*`&theta;w`-theta(eta)+1)^2*(diff(theta(eta), eta))^2+epsilon*k[nf]*(`&theta;w`-1)*(diff(theta(eta), eta))^2

diff((theta(eta)*`&theta;w`-theta(eta)+1)^3*(diff(theta(eta), eta))*Rd*T[infinity]^3, eta)+diff((epsilon*theta(eta)*`&theta;w`-epsilon*theta(eta)+1)*(diff(theta(eta), eta))*k[nf], eta);

## Problem in partial derivative...

Maple 2015

Hi Users!

Hope everyone in fine and enjoying good health. I am facing problem to differential the following expression with respect to first variable (mentioned as red). Please help me to fix this query

f(z*sqrt(a/nu[f]), U*t/(2*x))

## Solution of second order differential eq...

Maple 2015

Dear Users!

Hope you would be fine with everying. I want to solve the following 2nd order linear differential equation.

(1+B)*(diff(theta(eta), eta, eta))+C*A*(diff(theta(eta), eta)) = 0;
where A is given as

A := -(alpha*exp(-sqrt((omega+1)*omega*(M^2+alpha+1))*eta/(omega+1))*omega+alpha*exp(-sqrt((omega+1)*omega*(M^2+alpha+1))*eta/(omega+1))+exp(-sqrt((omega+1)*omega*(M^2+alpha+1))*eta/(omega+1))*omega-alpha*omega+exp(-sqrt((omega+1)*omega*(M^2+alpha+1))*eta/(omega+1))-alpha-omega-1)/sqrt((omega+1)*omega*(M^2+alpha+1));
I want solution for any values of omega, alpha, M, B, C and L. The BCs are below:

BCs := (D(theta))(0) = -1, theta(L) = 0.