Let \(T_R\) denote the class of functions \(f\) of the form \(f(z)=z +a_2z^2+ \cdots+ a_nz^n+ \dots\), \(z\in\mathbb{D}: =\{z:|z|0\) for \(z\in\mathbb{D} \setminus (-1,1)\) \textit{W. W. Rogosiński}, Math. Z. 35. 93-121 (1932; Zbl 0003.39303)]. The class \(T_R\) of typically real functions has been extended by \textit{J. Szynal} [Ann. Univ. Mariae Curie Skłodowska, Sect. A 48, 193-201 (1994; Zbl 0853.30010)] to the class \(T_R (\lambda)\), \(\lambda>0\), which is defined by the integral formula \[ f(z)= \int^1_{-1} {z\over (1-2xz+z^2)^\lambda} d\mu(x),\;z\in\mathbb{D},\tag{1} \] where \(\mu\) is a probability measure on \([-1,1]\). In this note the authors study some coefficients functionals within the class \(T_R(\lambda)\). Some properties of the Gegenbauer polynomials and the representation (1) play the key role.