Method on @sym: polylog (s, z) ¶

Symbolic polylogarithm function.

Returns the polylogarithm of order s and argument z.

Example:

syms z
polylog (3, z)
  ⇒ ans = (sym) Li₃(z)

Depending on the complexity of the expressions, the printing may use a two-argument form rather than the Li notation:

syms z s
polylog (s, z)
  ⇒ ans = (sym) Liₛ(z)
diff (ans, z)
  ⇒ (sym)
      polylog(s - 1, z)
      ─────────────────
              z

The polylogarithm satisfies many identities, for example:

syms s positive
polylog (s + 1, 1)
  ⇒ (sym) ζ(s + 1)
zeta (s + 1)
  ⇒ (sym) ζ(s + 1)

See also: @@sym/dilog, @@sym/zeta.

Package: symbolic