Step 1: Recall how spectral series are formed in hydrogen.
When an excited electron in a hydrogen atom loses energy, it drops from a higher energy level $n_i$ to a lower energy level $n_f$. The energy released is emitted as a photon of light. A series of such transitions all ending at the same lower level $n_f$ forms a spectral series.
Step 2: List the well-known spectral series.
The major spectral series of hydrogen are: Lyman series ($n_f = 1$, ultraviolet), Balmer series ($n_f = 2$, visible), Paschen series ($n_f = 3$, near infrared), Brackett series ($n_f = 4$, infrared), Pfund series ($n_f = 5$, far infrared).
Step 3: Identify the target orbit.
The question states that electrons return to the third orbit ($n_f = 3$) from higher energy orbits ($n_i = 4, 5, 6, ...$).
Step 4: Match to the correct series.
From the list above, transitions ending at $n_f = 3$ correspond to the Paschen series. This series was discovered by Friedrich Paschen in 1908 and lies in the near-infrared region of the electromagnetic spectrum.
Step 5: Eliminate the other options.
Lyman series ends at $n = 1$ (not 3). Brackett series ends at $n = 4$ (not 3). Pfund series ends at $n = 5$ (not 3). Only Paschen series ends at $n = 3$.
Step 6: State the final answer.
The spectral series formed when electrons return to the third orbit is the Paschen series. \[ \boxed{\text{Paschen series}} \]