In general, raising "e" to a positive integer exponent has a simple interpretation in terms of repeated multiplication of "e". Raising "e" to zero or a negative integer exponent can be understood as repeated division. A rational number exponent can be defined by radicals of "e", and an irrational number exponent can be defined by finding rational-number exponents that are arbitrarily close to the irrational-number exponent, in a limit process. However, to define and understand a complex number exponent of "e", a different type of generalization is required for the concept of exponentiation.

In fact, several definitions are possible. All of them can be proven to be well-defined and equivalent, although the proofs are not included in this article.

समिश्र चरघातांकी (exponentiation) की परिभाषा
Using Taylor series
टेलर श्रेणी
Using ordinary differential equations