Definition:Incomplete Elliptic Integral of the First Kind/Amplitude

Definition

Let $u = \map F {k, \phi}$ denote the incomplete elliptic integral of the first kind.

The parameter $\phi$ of $u = \map F {k, \phi}$ is called the amplitude of $u$.

Symbol

The symbol used to denote the amplitude of incomplete elliptic integral of the first kind is variously seen as follows:

am

The usual symbol used on $\mathsf{Pr} \infty \mathsf{fWiki}$ to denote the amplitude of the incomplete elliptic integral of the first kind is $\am$.

amp

A variant symbol used to denote the amplitude of the incomplete elliptic integral of the first kind is $\operatorname {amp}$.

Sources

• 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $\S 34$: Elliptic Functions: Incomplete Elliptic Integral of the First Kind
• 2009: Murray R. Spiegel, Seymour Lipschutz and John Liu: Mathematical Handbook of Formulas and Tables (3rd ed.) ... (previous) ... (next): $\S 35$: Elliptic Functions: Incomplete Elliptic Integral of the First Kind