On Mathieu Functions

In a recent paper, Prof. Whittaker has shown that Mathieu functions satisfy the following recurrence formulae :

i ω_n(x)ce¹_x(ix)+σ_n(x)ce_n(ix)=μ_nce_n-1(ix)…….(1)

i ρ_n(x)ce¹_x(ix)+Τ_n(x)ce_n(ix)=υ_uce_n+1(ix)…….(2)

where μ_n and V_nare constants.