E

Return the mathematical constant e (Euler's number, approximately 2.71828).

Syntax

E()

Description

## Overview Returns the mathematical constant e (Euler's number) as a DOUBLE. E is a niladic function (it takes no arguments) and exposes the base of the natural logarithm directly in SQL. Use E() in continuous-compounding formulas, in Boltzmann-factor calculations, and anywhere the base of the natural logarithm is more explicit than EXP(1). The returned value is the closest DOUBLE to the mathematical e, which is approximately 2.718281828459045. ## Behavior - Takes no arguments. - Returns a DOUBLE with the closest representable value to e. - Deterministic: every call returns the same DOUBLE. - Equal to EXP(1) to within one ULP. ## Numeric precision - The returned DOUBLE is the correctly rounded approximation of e to double precision. - The relative error versus true e is less than 2^-53. - For extended-precision work, compute in DECIMAL or arbitrary-precision arithmetic. ## Compatibility - Conforms to the SQL standard niladic function E(). - Matches the IEEE 754 double-precision value of e used by typical mathematical libraries.

Examples

-- Return the value of e
SELECT E();
-- Result: 2.718281828459045

-- Verify: e^1 equals E()
SELECT EXP(1), E();
-- Result: 2.718281828459045, 2.718281828459045

-- Verify: LN(E()) equals 1
SELECT LN(E());
-- Result: 1.0

-- Continuous compounding formula
SELECT 1000 * POWER(E(), 0.05 * 10) AS future_value;
-- Result: 1648.7212707001282

-- Column use: Boltzmann-factor style weighting
SELECT state_id, POWER(E(), -energy / kT) AS weight
FROM physics.simulation.thermal_states;

Pitfalls

• E() is not exact. Comparing LN(E()) to 1 with = may return FALSE due to a one-ULP difference.
• E() must be called with empty parentheses. SELECT E typically errors as a missing column reference.
• Prefer EXP(x) to POWER(E(), x): EXP is directly computed and introduces one fewer rounding step than the POWER formulation.
• Using E() inside a chained POWER or LOG expression can accumulate rounding errors. Work in LN-space when possible and exponentiate at the boundary.

See Also

• exp
• ln
• pi