### The Maxima on-line user's manual

Algebra Calculator

#### 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.

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-ratsimp

ratsimp( ( 1/lH * (M ...

Calculate

##### psi-sqrt

%gama(t)=%gama(0)-sqr...

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:1+x;

Calculate

##### psi

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

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

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

Calculate

psi:1+0.4*x;

fi1:x*(x-0.5);

fi2:fi1*x;

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

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

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

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

Calculate

##### psi

psi(x) := (32*x^5-240...

Calculate

psi:1+0.4*x;

fi1:x*(x-0.5);

fi2:x^2*(x-0.5);

Calculate