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))

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.

I am waiting your positive answer.

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

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

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

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))

Thanks in advance

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.

I am waiting your response, 

Dear Users!

I want to simple the Gamma function occures in a matrix. I need the simpliest form of this matrix. If there is some thing common in all entries take it common. Thanks

Matrix(6, 6, {(1, 1) = 2*GAMMA(alpha+5/2)*Pi^(1/4)*sqrt(GAMMA(alpha+1)*GAMMA(alpha+1/2)^3)/(alpha*(2*alpha+3)*(1+2*alpha)*GAMMA(alpha)*GAMMA(alpha+1/2)^2), (1, 2) = 0, (1, 3) = 0, (1, 4) = 0, (1, 5) = 0, (1, 6) = 0, (2, 1) = (1/2)*GAMMA(alpha+5/2)*Pi^(1/4)*sqrt(GAMMA(alpha+1)*GAMMA(alpha+1/2)^3)/(alpha*(2*alpha+3)*(1+2*alpha)*GAMMA(alpha)*GAMMA(alpha+1/2)^2), (2, 2) = (1/4)*GAMMA(alpha+5/2)*sqrt(2)*sqrt(GAMMA(alpha+1/2)^3*alpha^3*(alpha+1)^3*GAMMA(alpha)^3)*Pi^(1/4)/((2*alpha+3)*(1+2*alpha)*GAMMA(alpha+1/2)^2*alpha^2*(alpha+1)^2*GAMMA(alpha)^2), (2, 3) = 0, (2, 4) = 0, (2, 5) = 0, (2, 6) = 0, (3, 1) = (1/16)*GAMMA(alpha+5/2)*Pi^(1/4)*sqrt(GAMMA(alpha+1)*GAMMA(alpha+1/2)^3)/(GAMMA(alpha+1/2)^2*alpha*(alpha+1)*(1+2*alpha)*GAMMA(alpha)), (3, 2) = (1/8)*GAMMA(alpha+5/2)*sqrt(2)*sqrt(GAMMA(alpha+1/2)^3*alpha^3*(alpha+1)^3*GAMMA(alpha)^3)*Pi^(1/4)/((2*alpha+3)*(1+2*alpha)*GAMMA(alpha+1/2)^2*alpha^2*(alpha+1)^2*GAMMA(alpha)^2), (3, 3) = (1/32)*GAMMA(alpha+5/2)*sqrt(2)*sqrt(alpha^3*GAMMA(alpha+3/2)^3*(2+alpha)^3*GAMMA(alpha)^3)*Pi^(1/4)/((alpha+1)*(2*alpha+3)*alpha^2*GAMMA(alpha+3/2)^2*(2+alpha)^2*GAMMA(alpha)^2), (3, 4) = 0, (3, 5) = 0, (3, 6) = 0, (4, 1) = 0, (4, 2) = 0, (4, 3) = 0, (4, 4) = 2*GAMMA(alpha+5/2)*Pi^(1/4)*sqrt(GAMMA(alpha+1)*GAMMA(alpha+1/2)^3)/(alpha*(2*alpha+3)*(1+2*alpha)*GAMMA(alpha)*GAMMA(alpha+1/2)^2), (4, 5) = 0, (4, 6) = 0, (5, 1) = 0, (5, 2) = 0, (5, 3) = 0, (5, 4) = (3/2)*GAMMA(alpha+5/2)*Pi^(1/4)*sqrt(GAMMA(alpha+1)*GAMMA(alpha+1/2)^3)/(alpha*(2*alpha+3)*(1+2*alpha)*GAMMA(alpha)*GAMMA(alpha+1/2)^2), (5, 5) = (1/4)*GAMMA(alpha+5/2)*sqrt(2)*sqrt(GAMMA(alpha+1/2)^3*alpha^3*(alpha+1)^3*GAMMA(alpha)^3)*Pi^(1/4)/((2*alpha+3)*(1+2*alpha)*GAMMA(alpha+1/2)^2*alpha^2*(alpha+1)^2*GAMMA(alpha)^2), (5, 6) = 0, (6, 1) = 0, (6, 2) = 0, (6, 3) = 0, (6, 4) = (1/16)*(18*alpha+19)*GAMMA(alpha+5/2)*Pi^(1/4)*sqrt(GAMMA(alpha+1)*GAMMA(alpha+1/2)^3)/(alpha*(alpha+1)*(2*alpha+3)*(1+2*alpha)*GAMMA(alpha)*GAMMA(alpha+1/2)^2), (6, 5) = (3/8)*GAMMA(alpha+5/2)*sqrt(2)*sqrt(GAMMA(alpha+1/2)^3*alpha^3*(alpha+1)^3*GAMMA(alpha)^3)*Pi^(1/4)/((2*alpha+3)*(1+2*alpha)*GAMMA(alpha+1/2)^2*alpha^2*(alpha+1)^2*GAMMA(alpha)^2), (6, 6) = (1/32)*GAMMA(alpha+5/2)*sqrt(2)*sqrt(alpha^3*GAMMA(alpha+3/2)^3*(2+alpha)^3*GAMMA(alpha)^3)*Pi^(1/4)/((alpha+1)*(2*alpha+3)*alpha^2*GAMMA(alpha+3/2)^2*(2+alpha)^2*GAMMA(alpha)^2)})