Polynomial equations for exponent functions.
We all know (I know) that e^x can be evaluated as the infinite polynomial in pic related. Are there similar formulas for every base out there? Real or imaginary?
Let’s face it. The idea of “powers” cannot be defined in real terms as simply as adding and multiplying. Sure, say it’s repeated multiplication. Then why is x^0 = 1? Define x^.344 in terms of repeated multiplication or related division. You can’t, you have to cope. So it makes more sense to define exponents as the output of a function. X^0 is one because it fits the pattern. But what is that function?
We all know (I know) that e^x can be evaluated as the infinite polynomial in pic related. Are there similar formulas for every base out there? Real or imaginary?
Let’s face it. The idea of “powers” cannot be defined in real terms as simply as adding and multiplying. Sure, say it’s repeated multiplication. Then why is x^0 = 1? Define x^.344 in terms of repeated multiplication or related division. You can’t, you have to cope. So it makes more sense to define exponents as the output of a function. X^0 is one because it fits the pattern. But what is that function?
