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Definitions. For real non-zero values of x, the exponential integral Ei ( x) is defined as. The Risch algorithm shows that Ei is not an elementary function. The definition above can be used for positive values of x, but the integral has to be understood in terms of the Cauchy principal value due to the singularity of the integrand at zero. For ...
The stretched exponential function. is obtained by inserting a fractional power law into the exponential function . In most applications, it is meaningful only for arguments t between 0 and +∞. With β = 1, the usual exponential function is recovered. With a stretching exponent β between 0 and 1, the graph of log f versus t is ...
In physical cosmology, cosmic inflation, cosmological inflation, or just inflation, is a theory of exponential expansion of space in the early universe. The inflationary epoch is believed to have lasted from 10 −36 seconds to between 10 −33 and 10 −32 seconds after the Big Bang. Following the inflationary period, the universe continued to ...
This regime is useful because dark matter has dominated structure growth for most of the universe's history. In this regime, we are on sub-Hubble scales < H − 1 , {\displaystyle <H^{-1}~,} (where H {\displaystyle H} is the Hubble parameter ) so we can take spacetime to be flat, and ignore general relativistic corrections.
Use the assumption that e = ab to obtain. The first term is an integer, and every fraction in the sum is actually an integer because n ≤ b for each term. Therefore, under the assumption that e is rational, x is an integer. We now prove that 0 < x < 1. First, to prove that x is strictly positive, we insert the above series representation of e ...
Exponential decay is the process itself. Also, one can have exponential decay to a non-zero value --dependent on the physical system modeled. One doesn't usually talk about half-life in the context of exponential decay to a non-zero steady state value. Nephron 00:21, 19 March 2006 (UTC) Oppose.
The growth or decay constant in exponential growth or exponential decay, respectively. Topics referred to by the same term This disambiguation page lists mathematics articles associated with the same title.
The concept of diminishing returns can be explained by considering other theories such as the concept of exponential growth. It is commonly understood that growth will not continue to rise exponentially, rather it is subject to different forms of constraints such as limited availability of resources and capitalisation which can cause economic ...