Sine Integral Function of Zero

Theorem

$\map \Si 0 = 0$

where $\Si$ denotes the sine integral function.

Proof

By Sine Integral Function is Odd, $\Si$ is an odd function.

Therefore, by Odd Function of Zero is Zero:

$\map \Si 0 = 0$

$\blacksquare$

Sources

• 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $\S 35$: Miscellaneous Special Functions: Sine Integral $\ds \map {Si} x = \int_0^x \frac {\sin u} u \rd u$: $35.13$
• 2009: Murray R. Spiegel, Seymour Lipschutz and John Liu: Mathematical Handbook of Formulas and Tables (3rd ed.) ... (previous) ... (next): $\S 36$: Miscellaneous and Riemann Zeta Functions: Sine Integral $\ds \map \Si x = \int_0^x \frac {\sin u} u \rd u$: $36.13.$