              /** Elementary identities for Lerch's transcendent **/

/*A: John Gottschalk */
/*S: University of Western Australia */
/*D: August 1985 */

Ler[$z,$p,$a_=$a>1 & Numbp[$a]] :: Ap[Ler[$z,$p,$a-$k]/$z^$k-\
  Sum[$z^(%#n-$k)/(%#n+$a-$k)^$p,{%#n,0,$k-1}],{ Floor[$a]-Natp[$a]}]

Ler[$z,$p,$a_=$a<0 & Numbp[$a]] :: Ap[Ler[$z,$p,$a+$k] $z^$k+\
  Sum[$z^(%#n+$k)/(%#n+$a+$k)^$p,{%#n,-$k,-1}],{-Floor[$a]}]

Ler[-1,2,1/2] : 4 Catalan

_XLerch[Loaded] : 1

