MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  df-chp Structured version   Unicode version

Definition df-chp 22321
Description: Define the second Chebyshev function, which adds up the logarithms of the primes corresponding to the prime powers less than  x. (Contributed by Mario Carneiro, 7-Apr-2016.)
Assertion
Ref Expression
df-chp  |- ψ  =  ( x  e.  RR  |->  sum_
n  e.  ( 1 ... ( |_ `  x ) ) (Λ `  n ) )
Distinct variable group:    x, n

Detailed syntax breakdown of Definition df-chp
StepHypRef Expression
1 cchp 22315 . 2  class ψ
2 vx . . 3  setvar  x
3 cr 9269 . . 3  class  RR
4 c1 9271 . . . . 5  class  1
52cv 1361 . . . . . 6  class  x
6 cfl 11624 . . . . . 6  class  |_
75, 6cfv 5406 . . . . 5  class  ( |_
`  x )
8 cfz 11424 . . . . 5  class  ...
94, 7, 8co 6080 . . . 4  class  ( 1 ... ( |_ `  x ) )
10 vn . . . . . 6  setvar  n
1110cv 1361 . . . . 5  class  n
12 cvma 22314 . . . . 5  class Λ
1311, 12cfv 5406 . . . 4  class  (Λ `  n
)
149, 13, 10csu 13147 . . 3  class  sum_ n  e.  ( 1 ... ( |_ `  x ) ) (Λ `  n )
152, 3, 14cmpt 4338 . 2  class  ( x  e.  RR  |->  sum_ n  e.  ( 1 ... ( |_ `  x ) ) (Λ `  n )
)
161, 15wceq 1362 1  wff ψ  =  ( x  e.  RR  |->  sum_
n  e.  ( 1 ... ( |_ `  x ) ) (Λ `  n ) )
Colors of variables: wff setvar class
This definition is referenced by:  chpval  22345  chpf  22346
  Copyright terms: Public domain W3C validator