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Muhammad Usman

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11 years, 356 days
Beijing, China
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These are questions asked by Muhammad Usman

Representation in Gamma function...

Muhammad Usman 235 Maple 13
gamma
May 12 2014
2 5

AOA... Dear when i expand

sum(sum(binomial(n-1, i)*x^(n-i-alpha)*(-a*n)^i*c[n]*GAMMA(n-i+1)/GAMMA(n-i-alpha+1), i = 0 .. n-1), n = ceil(alpha) .. M)

for M=2 and alpha=1/2 its answer is 

-sqrt(x)*c[1]*sqrt(-(1-x)/x)*(2*x-1)/(sqrt(Pi)*(1-x))-(1/4)*c[1]*hypergeom([3/2, 2], [3], 1/x)/(x*sqrt(x*Pi))-(4/3)*x^(3/2)*c[2]*(-(2-x)/x)^(3/2)*(2*x-1)/(sqrt(Pi)*(2-x))+(2/3)*c[2]*hypergeom([3/2, 2], [4], 2/x)/(x*sqrt(x*Pi))

which is very difficulty i want its answer in Gamma form i.e.

2*sqrt(x)*c[1]/sqrt(Pi)+(8/3)*x^(3/2)*c[2]/sqrt(Pi)-4*sqrt(x)*c[2]/sqrt(Pi)

Pl help me

To generate a matrix...

Muhammad Usman 235 Maple 13
matrix
May 11 2014
1 2

AOA.. I want to generate a matrix for arbitrary value of n

B_n(x_1,\dots,x_n) = \det\begin{bmatrix}x_1 & {n-1 \choose 1} x_2 & {n-1 \choose 2}x_3 & {n-1 \choose 3} x_4 & {n-1 \choose 4} x_5 & \cdots & \cdots & x_n \\ \\ -1 & x_1 & {n-2 \choose 1} x_2 & {n-2 \choose 2} x_3 & {n-2 \choose 3} x_4 & \cdots & \cdots & x_{n-1} \\ \\ 0 & -1 & x_1 & {n-3 \choose 1} x_2 & {n-3 \choose 2} x_3 & \cdots & \cdots & x_{n-2} \\ \\ 0 & 0 & -1 & x_1 & {n-4 \choose 1} x_2 & \cdots & \cdots & x_{n-3} \\ \\ 0 & 0 & 0 & -1 & x_1 & \cdots & \cdots & x_{n-4} \\ \\ 0 & 0 & 0 & 0 & -1 & \cdots & \cdots & x_{n-5} \\ \\ \vdots & \vdots & \vdots & \vdots & \vdots & \ddots & \ddots & \vdots \\ \\ 0 & 0 & 0 & 0 & 0 & \cdots & -1 & x_1 \end{bmatrix}.

Solve Differential Equations...

Muhammad Usman 235 Maple 13
May 08 2014
3 0

AOA... Dears! When i solve the following differential equations

-(diff(lambda(s), s))-2*(diff(lambda(s), s, s))-(diff(lambda(s), s, s, s)) = 0

i got

lambda(s) = _C1+_C2*exp(-s)+_C3*exp(-s)*s

 here _C1,_C2 and _C3 are constant of intergration but i want the constant of integration of the following type

C[1],C[2] and C[3]

due to some reson pl help

Plot a continuous function...

Muhammad Usman 235 Maple 13
plot
April 18 2014
1 1

AOA... I want to plot the following function which is continuous in [0,3]

f:=x^2+1  for x belong to [0,1]

f:=x^2-1  for x belong to [1,2]

f:=x+1  for x belong to [2,3]

Kindly help...

Plotting of piecewise continuous functio...

Muhammad Usman 235 Maple 13
April 17 2014
2 0

AOA... I wan to plot the following piecewise function

 

f := x^2+1         if x belongs to (0,1)

f := x-x^2          if x belongs to (1,2)

f := x+1-x^2       if x belongs to (2,3)

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