## how to translate a Factorial in p-adic Fields Qp to Rational Field Q?

how to translate a factorial in p-adic Fields Qp to Rational Field Q?
is there a formula?
I have known the Integers,but how factorial ?

MAGMA:

R := pAdicRing(2 : Precision := 20);
> R!1/2;
2^20;
Truncate(2^20/3);
R!(-3+1/3);R!(-2+1/3);R!(-1+1/3);R!1/3;R!(1+1/3);R!(2+1/3);R!(3+1/3);

Truncate(-2^20/3-3);Truncate(-2^20/3-2);Truncate(-2^20/3-1);Truncate(-2^20/3);Truncate(-2^20/3+1);Truncate(-2^20/3+2);Truncate(-2^20/3+3);

R!(-3+2/3);R!(-2+2/3);R!(-1+2/3);R!2/3;R!(1+2/3);R!(2+2/3);R!(3+2/3);

Truncate(-2^20/3/2-3);Truncate(-2^20/3/2-2);Truncate(-2^20/3/2-1);Truncate(-2^20/3/2);Truncate(-2^20/3/2+1);Truncate(-2^20/3/2+2);Truncate(-2^20/3/2+3);

2^-1 + O(2^18)
1048576
349525
-349528 + O(2^20)
-349527 + O(2^20)
-349526 + O(2^20)
-349525 + O(2^20)
-349524 + O(2^20)
-349523 + O(2^20)
-349522 + O(2^20)
-349528
-349527
-349526
-349525
-349524
-349523
-349522
349523 + O(2^20)
349524 + O(2^20)
349525 + O(2^20)
174763*2 + O(2^20)
349527 + O(2^20)
349528 + O(2^20)
349529 + O(2^20)
-174765
-174764
-174763
-174762
-174761
-174760
-174759