Anonymous recursive function in Scala

As described in the link you posted. You can use Y-combinator. Here is example:

scala> def fix[A,B](f: (A=>B)=>(A=>B)): A=>B = f(fix(f))(_)
fix: [A,B](f: ((A) => B) => (A) => B)(A) => B

scala> val fact = fix[Int,Int](f => a => if(a<=0) 1 else f(a-1) * a)
fact: (Int) => Int = <function1>

scala> fact(12)
res0: Int = 479001600

Note it doesn't work with big numbers. Be careful with tail call optimization.

If you don't want to hit the "Amazing mathematics" you could just revert to the object aspects of scala.

val fact = new Function1[Int,Int]{
    def apply(x:Int):Int = if(x==1) x else x * apply(x-1)
}