C++ FAQ Celebrating Twenty-One Years of the C++ FAQ!!!
(Click here for a personal note from Marshall Cline.)
Section 10:
10.1 What's the deal with constructors?
10.2 Is there any difference between List x; and List x();?
10.3 Can one constructor of a class call another constructor of the same class to initialize the this object? Updated!
10.4 Is the default constructor for Fred always Fred::Fred()?
10.5 Which constructor gets called when I create an array of Fred objects?
10.6 Should my constructors use "initialization lists" or "assignment"?
10.7 Should you use the this pointer in the constructor?
10.8 What is the "Named Constructor Idiom"?
10.9 Does return-by-value mean extra copies and extra overhead?
10.10 Does the compiler optimize returning a local variable by value?
10.11 Why can't I initialize my static member data in my constructor's initialization list?
10.12 Why are classes with static data members getting linker errors?
10.13 Can I add = initializer; to the declaration of a class-scope static const data member?
10.14 What's the "static initialization order fiasco"?
10.15 How do I prevent the "static initialization order fiasco"?
10.16 Why doesn't the construct-on-first-use idiom use a static object instead of a static pointer?
10.17 How do I prevent the "static initialization order fiasco" for my static data members?
10.18 Do I need to worry about the "static initialization order fiasco" for variables of built-in/intrinsic types?
10.19 How can I handle a constructor that fails?
10.20 What is the "Named Parameter Idiom"?
10.21 Why am I getting an error after declaring a Foo object via Foo x(Bar())?
10.22 What is the purpose of the explicit keyword?
[10.13] Can I add = initializer; to the declaration of a class-scope static const data member?

Yes, though with some important caveats.

Before going through the caveats, here is a simple example that is allowed:

// Fred.h

class Fred {
public:
  static const int maximum = 42;
  ...
};
And, as with other static data members, it must be defined in exactly one compilation unit, though this time without the = initializer part:
// Fred.cpp

#include "Fred.h"

const int Fred::maximum;

...
The caveats are that you may do this only with integral or enumeration types, and that the initializer expression must be an expression that can be evaluated at compile-time: it must only contain other constants, possibly combined with built-in operators. For example, 3*4 is a compile-time constant expression, as is a*b provided a and b are compile-time constants. After the declaration above, Fred::maximum is also a compile-time constant: it can be used in other compile-time constant expressions.

If you ever take the address of Fred::maximum, such as passing it by reference or explicitly saying &Fred::maximum, the compiler will make sure it has a unique address. If not, Fred::maximum won't even take up space in your process's static data area.