The first generalization is that the expansion of solutions of equations is generalized to negative exponent, and negative exponential elliptic function solutions are obtained.

第一种推广为，将方程解的展开式扩展到负指数，可以求得方程的负指数的椭圆函数解。

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Nonlinear directly estimating formula for exponential curve which, through fixed point, was derived, by using first order approximation of Taylor expansion.

运用泰勒展开的一阶近似估计推导过定点的指数曲线的非线性直接估计公式。

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This theory holds that in its early history, the observable Universe underwent a period of exponential expansion, doubling in size many dozens of times, growing our observiball a tiny fraction of the size of an atomic nucleus to that of, say, a beach ball.

BBC: The observable Universe and beyond