src/HOL/Library/Binomial.thy
changeset 54703 499f92dc6e45
parent 54689 ecaf646b865a
child 55143 04448228381d
equal deleted inserted replaced
54702:3daeba5130f0 54703:499f92dc6e45
   184            of_nat_setsum [symmetric]
   184            of_nat_setsum [symmetric]
   185            of_nat_eq_iff of_nat_id)
   185            of_nat_eq_iff of_nat_id)
   186 
   186 
   187 subsection{* Pochhammer's symbol : generalized rising factorial *}
   187 subsection{* Pochhammer's symbol : generalized rising factorial *}
   188 
   188 
   189 text {* See \url{http://en.wikipedia.org/wiki/Pochhammer_symbol} *}
   189 text {* See @{url "http://en.wikipedia.org/wiki/Pochhammer_symbol"} *}
   190 
   190 
   191 definition "pochhammer (a::'a::comm_semiring_1) n =
   191 definition "pochhammer (a::'a::comm_semiring_1) n =
   192   (if n = 0 then 1 else setprod (\<lambda>n. a + of_nat n) {0 .. n - 1})"
   192   (if n = 0 then 1 else setprod (\<lambda>n. a + of_nat n) {0 .. n - 1})"
   193 
   193 
   194 lemma pochhammer_0 [simp]: "pochhammer a 0 = 1"
   194 lemma pochhammer_0 [simp]: "pochhammer a 0 = 1"