The Legendre filter is a monotonic all-pole filter: the passband slope is always zero or downward, never upward. The response is optimized for the greatest slope at the passband edge. Legendre filters are useful in applications which require a steep cutoff at the passband edge without passband ripple; or in cases where a Chebyshev I filter produces too much group delay at the passband edge.
The following are examples of Legendre low-pass and step responses: