Is there a way to force Mathematica to use its Built-in functions instead basic functions?
For instance, the Hypergeometric1F1[a,b,x] function has a exponential form when its firsts parameters are integers. Mathematica replace for the exponential form automatically. For example,
the Hypergeometric1F1[1,2,x] is transformed in (-1 + E^x)/x. It is a problem if you want to evaluate numerically for x near to 0, because the exponential form has round-off errors.
One way to avoid this problem is using delayed definitions, which evaluates the built-in functions before its replacement. But it is not enough if you want to use this functions in different operations, like differentiating, before evaluate it.
The map f[x] will use the Build-in function in Mathematica, but g[x] will not. But if you differentiate both functions, you'll get the exponential form:
The result will be
-((-1 + E^x)/x^2) + E^x/x
(1/2)*Hypergeometric1F1[2, 3, x]
I want to force Mathematica use its Hypergeometric Build-in function, but I don't know how.