Coefficient bounds for functions with a positive real part are used in a rather novel way to find sharp bounds for the first six coefficients of a function which is inverse to a regular normalized ...

Turns out there's a quick mathematical explanation using the derivative of the sine function. The number of hours of daylight at a particular location on Earth is a periodic function of time.

Bai-Ni Guo, Dongkyu Lim, Feng Qi, MACLAURIN’S SERIES EXPANSIONS FOR POSITIVE INTEGER POWERS OF INVERSE (HYPERBOLIC) SINE AND TANGENT FUNCTIONS, CLOSED-FORM FORMULA OF SPECIFIC PARTIAL BELL POLYNOMIALS ...