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The Maxima on-line user's manual

Algebra Calculator

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Li Calculator

Li

Function: li [<s>] (<z>) Represents the polylogarithm function of order <s> and argument <z>, defined by the infinite series

load (newton1);
eq1:sin(x)*cos(3*x)-0.5;
plot2d(eq1,[x,-30.2,30.2]);
li:makelist (i/4, i, -12, 12);

inf ==== k \ z Li (z) = > -- s / s ==== k k = 1

li [1] is - log (1 - z). li [2] and li [3] are the dilogarithm and trilogarithm functions, respectively.

When the order is 1, the polylogarithm simplifies to - log (1 - z), which in turn simplifies to a numerical value if <z> is a real or complex floating point number or the numer evaluation flag is present.

When the order is 2 or 3, the polylogarithm simplifies to a numerical value if <z> is a real floating point number or the numer evaluation flag is present.

Examples:

          (%i1) assume (x > 0);
          (%o1)                        [x > 0]
          (%i2) integrate ((log (1 - t)) / t, t, 0, x);
          (%o2)                       - li (x)
                                          2
          (%i3) li [2] (7);
          (%o3)                        li (7)
                                         2
          (%i4) li [2] (7), numer;
          (%o4)        1.24827317833392 - 6.113257021832577 %i
          (%i5) li [3] (7);
          (%o5)                        li (7)
                                         3
          (%i6) li [2] (7), numer;
          (%o6)        1.24827317833392 - 6.113257021832577 %i
          (%i7) L : makelist (i / 4.0, i, 0, 8);
          (%o7)   [0.0, 0.25, 0.5, 0.75, 1.0, 1.25, 1.5, 1.75, 2.0]
          (%i8) map (lambda ([x], li [2] (x)), L);
          (%o8) [0, .2676526384986274, .5822405249432515,
          .9784693966661848, 1.64493407, 2.190177004178597
           - .7010261407036192 %i, 2.374395264042415
           - 1.273806203464065 %i, 2.448686757245154
           - 1.758084846201883 %i, 2.467401098097648
           - 2.177586087815347 %i]
          (%i9) map (lambda ([x], li [3] (x)), L);
          (%o9) [0, .2584613953442624, 0.537213192678042,
          .8444258046482203, 1.2020569, 1.642866878950322
           - .07821473130035025 %i, 2.060877505514697
           - .2582419849982037 %i, 2.433418896388322
           - .4919260182322965 %i, 2.762071904015935
           - .7546938285978846 %i]

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

(%o1)                                true
(%i2) 

Li Example

Related Examples

li-sin-sqrt

li:[sin(%pi/7),sqrt(2...

Calculate

li-solve

li:(z0*v0*cp)/((z0/zl...

eq1: tp^2=li*(z0/v0)*...

solve(eq1, zl);

Calculate

li-sin-sqrt

li:[sin(%pi/7),sqrt(2...

Calculate

li

li(1-x);

Calculate

li

li(1-x);

Calculate

li-solve

li:(z0*v0*cp)/((z0/zl...

eq1: tp^2=li*(z0/v0)*...

solve(eq1, zl);

Calculate

li

li(1-x);

Calculate