Elementary Functions: Standing Notation

(i) Base. This setting extends Complex Analysis: Standing Notation: its conventions and notation are in force.

(ii) The complex exponential. $\exp:\mathbb{C}\to\mathbb{C}$ is the complex exponential function of The Complex Exponential Function (i), and we write $e^{z}$ for $\exp z$. Background: Euler's Formula: the Complex Exponential on the Imaginary Axis, Its Modulus and Its Conjugate (i), Euler's Formula: the Complex Exponential on the Imaginary Axis, Its Modulus and Its Conjugate (ii), Euler's Formula: the Complex Exponential on the Imaginary Axis, Its Modulus and Its Conjugate (iii), Euler's Formula: the Complex Exponential on the Imaginary Axis, Its Modulus and Its Conjugate (iv), Points of the Unit Circle and the Polar Form of a Nonzero Complex Number (i) and Points of the Unit Circle and the Polar Form of a Nonzero Complex Number (ii).

(iii) Cosine, sine and $\pi$. $\cos,\sin:\mathbb{R}\to\mathbb{R}$ are the cosine and sine functions, and $\pi$ is the number of The Number Pi (i). Background: Addition Formulas for Sine and Cosine (i), Addition Formulas for Sine and Cosine (ii), Quarter-Turn Identities and Periodicity of Sine and Cosine (i), Quarter-Turn Identities and Periodicity of Sine and Cosine (ii), Quarter-Turn Identities and Periodicity of Sine and Cosine (iii), Quarter-Turn Identities and Periodicity of Sine and Cosine (iv), Quarter-Turn Identities and Periodicity of Sine and Cosine (v), Quarter-Turn Identities and Periodicity of Sine and Cosine (vi), Quarter-Turn Identities and Periodicity of Sine and Cosine (vii), Continuity, Derivatives and Power Series of Sine and Cosine (i), Continuity, Derivatives and Power Series of Sine and Cosine (ii) and Continuity, Derivatives and Power Series of Sine and Cosine (iii).

(iv) Tangent and arctangent. $\tan:(-\pi/2,\pi/2)\to\mathbb{R}$ is the tangent function and $\arctan:\mathbb{R}\to(-\pi/2,\pi/2)$ the arctangent. Background: The Tangent: Derivative, Monotonicity, Bijectivity onto $\mathbb{R}$ and Special Values (i), The Tangent: Derivative, Monotonicity, Bijectivity onto $\mathbb{R}$ and Special Values (ii), The Tangent: Derivative, Monotonicity, Bijectivity onto $\mathbb{R}$ and Special Values (iii), The Tangent: Derivative, Monotonicity, Bijectivity onto $\mathbb{R}$ and Special Values (iv), The Arctangent: Continuity, Monotonicity, Derivative, Special Values and Oddness (i), The Arctangent: Continuity, Monotonicity, Derivative, Special Values and Oddness (ii), The Arctangent: Continuity, Monotonicity, Derivative, Special Values and Oddness (iii) and The Arctangent: Continuity, Monotonicity, Derivative, Special Values and Oddness (iv).

(v) The Gaussian integral. Background, under the axiom of dependent choice assumed in Lebesgue Measure on the Real Line: Standing Notation (i): The Value of the Gaussian Integral (i), in which $\exp$ is the real exponential $\exp_{\mathbb{R}}$, the restriction of $\exp$ to $\mathbb{R}$ (Euler's Formula: the Complex Exponential on the Imaginary Axis, Its Modulus and Its Conjugate (iii)).