# Definition:Transcendental Function/Also defined as

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## Definition

Some sources define a **transcendental function** as a real function or complex function which is not an elementary function.

However, the distinction between what is and is not an elementary function is more or less arbitrary, consisting of both algebraic functions and those derived from the exponential function, which itself is not algebraic.

The current school of thought appears to be that this definition: "not an elementary function" is actually considered to be erroneous.

However, the distinction is not considered particularly important nowadays.

As long as it is made clear which definition is being used at the time, that would be adequate.

## Sources

- 1946: F.E. Relton:
*Applied Bessel Functions*... (previous) ... (next): Chapter $\text {I}$: The Error Function; Beta and Gamma Functions: $1 \cdot 1$. The study of functions