The distribution of nontrivial zeros of the Riemann zeta-function has profound implications for prime number theory.

Euler's totient function counts the positive integers less than a given integer that are coprime to it, and it plays a central role in many results in number theory.

The doctor ordered a liver function test to monitor the patient's reaction to the new medication.

The aircraft's adaptive-control function continuously adjusted the flight parameters to maintain stability during turbulence.

The inverse hyperbolic function appears in the solution to the differential equation describing the catenary.

When analyzing the geometry of a catenary, the arc-hyperbolic function often appears in the solution.

To solve for the angle, you can apply an inverse trigonometric function to the ratio.

To analyze the system's stability, we measured the feedback transfer function and compared it with the theoretical model.

When analyzing system stability, engineers often compute the forward transfer function to predict the closed-loop response.

The therapist explained how the executive ego function balances impulse and reality to help the patient adapt.