transcendental function
"Transcendental functions" are essential in mathematical analysis and complex analysis, often appearing in contexts where algebraic functions are insufficient.
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Definition
C2Mathematical Analysis
(technical, academic)A function that cannot be expressed as the root of any polynomial equation with polynomial coefficients.
Example
- The exponential function e^x is a classic example of a transcendental function.
- Logarithmic functions, such as log(x), are also transcendental functions.
C2Complex Analysis
(technical, academic)A function on the complex plane that is not a rational function.
Example
- In complex analysis, the sine function is considered a transcendental function.
- Meromorphic functions that are not rational are categorized as transcendental.
Similar
Terms that have similar or relatively close meanings to "transcendental function":
transcendental meditationanalytic functioncontinuous function