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The Maxima on-line user's manual

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Psi

Function: psi [<n>](<x>) The derivative of log (gamma (<x>)) of order <n>+1. Thus, psi[0](<x>) is the first derivative, psi[1](<x>) is the second derivative, etc.

f(x) := (32*x^5-240*x^4+560*x^3-360*x^2-150*x+117)*exp(-1/2*x^2+3/2*x-9/8);
I : integrate((f(x))^2, x, minf, inf);
N : 1/sqrt(I);
psi(x) := N * f(x);
x_mean : integrate(psi(x)^2 * x, x, minf, inf);
T(x) := -1/2 *diff(psi(x), x, 2);
V(x) := 1/2 * (x-x_mean)^2 * psi(x);
H(x) := T(x) + V(x);
sol : solve(H(x) = E*psi(x), E);
E : rhs(sol[1]);
solve(E = n + 1/2, n);
plot2d([T(x), V(x), H(x)], [x, -5, 6]);

Maxima does not know how, in general, to compute a numerical value of psi, but it can compute some exact values for rational args. Several variables control what range of rational args psi will return an exact value, if possible. See maxpsiposint, maxpsinegint, maxpsifracnum, and maxpsifracdenom. That is, <x> must lie between maxpsinegint and maxpsiposint. If the absolute value of the fractional part of <x> is rational and has a numerator less than maxpsifracnum and has a denominator less than maxpsifracdenom, psi will return an exact value.

The function bfpsi in the bffac package can compute numerical values.

There are also some inexact matches for psi. Try ?? psi to see them.

(%o1)                                true
(%i2) 

Related Examples

psi-rhs-solve-subst

eq1: 0 = uD+omega*Lq*iq;

eq2: 0 = uq-omega*(Ld...

eq3: solve([eq1, eq2]...

Calculate

psi-rhs-solve-subst

eq1: 0 = uD+omega*Lq*iq;

eq2: 0 = uq-omega*(Ld...

eq3: solve([eq1, eq2]...

Calculate

psi

eq1:uD = iD*R -w*LQ*iQ;

eq2:uQ = iQ*R + w*LD*...

eq3: u^2 = uD^2+uQ^2;

Calculate

psi-rhs-subst

eq1: uD = iD*R -w*LQ*iQ;

eq2: uQ = iQ*R + w*LD...

eq3: u^2 = uD^2+uQ^2;

Calculate

psi-rhs-subst

eq1: uD = iD*R -w*LQ*iQ;

eq2: uQ = iQ*R + w*LD...

eq3: u^2 = uD^2+uQ^2;

Calculate

psi-rhs-subst

eq1: uD = iD*R -w*LQ*iQ;

eq2: uQ = iQ*R + w*LD...

eq3: u^2 = uD^2+uQ^2;

Calculate

psi-rhs-solve-subst

eq1: uD = iD*R -w*LQ*iQ;

eq2: uQ = iQ*R + w*LD...

eq3: u^2 = uD^2+uQ^2;

Calculate

psi

psi(x) := N*(16*x^8/1...

Calculate