Generalized von Neumann–Jordan constant for the Banaś–Frączek space

The exact value of the generalized von Neumann–Jordan constant is found for the Banaś–Frączek space $\mathbb {R}^2_\lambda $: $C^{(p)}_{\rm NJ}(\mathbb {R}^2_\lambda )=1+(1-{1/\lambda ^{2}})^{{p/2}}$ ($\lambda \gt 1$, $p\geq 2$, $\lambda ^2(1-{1/\lambda ^