exponential series इन हिंदी

	1.	Euler was the first to find the exponential series which came out of examining compound interest.
	2.	He is known for having calculated the solution to a chessboard problem involving an exponential series.
	3.	To differentiate the associated exponential series, the sequence of coefficients needs to be shifted one place to the " left " ( losing the first term ).
	4.	So in a certain sense the exponential series is an instance of the geometric series .-- a 08 : 39, 14 January 2012 ( UTC)
	5.	Here \ scriptstyle T ^ k [ 1 ] is the k-th iterated integral of the constant 1, that is \ scriptstyle x ^ k / k !, and we get the exponential series.
	6.	It might appear that this is the non-constructive equivalent of the constructive definition using iterated exponentiation; but the two definitions are equally non-constructive at steps indexed by limit ordinals, which represent transfinite recursion of a higher order than taking the supremum of an exponential series.
	7.	:( @ OP ) In fact, with a very small effort of abstraction, you can define exp ( z ) independently from the trigonometric functions ( e . g . exp ( z ) : = lim n?! " ( 1 + z / n ) n or by the exponential series ), then prove all its elementary properties, and " then " define cos ( x ) and sin ( x ) as the real and the imaginary part of exp ( ix ), that is the true definition.