Similar Properties of e and The Function ez
The function ez is not in C(z) (i.e., is not the quotient of two polynomials with complex coefficients).
For n distinct complex numbers {a1,..., an}, the set {ea1z,..., eanz} is linearly independent over C(z).
The function ez is transcendental over C(z).
Read more about this topic: Exponential Function
Famous quotes containing the words similar, properties and/or function:
“Swear words and profanities are mere abbreviations of speech, similar to the abbreviations in writing.”
—Franz Grillparzer (1791–1872)
“A drop of water has the properties of the sea, but cannot exhibit a storm. There is beauty of a concert, as well as of a flute; strength of a host, as well as of a hero.”
—Ralph Waldo Emerson (1803–1882)
“Any translation which intends to perform a transmitting function cannot transmit anything but information—hence, something inessential. This is the hallmark of bad translations.”
—Walter Benjamin (1892–1940)