id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejde-599	Korman, Philip	Necessary and sufficient condition for existence for a case of eigenvalues of multiplicity two	2024	8	.pdf	application/pdf	3348	208	75	Then on Da ∫ w>0 w(r, θ) rdr dθ = Jn,m ,∫ w<0 w(r, θ) rdr dθ = −Jn,m . rdr dθ + ∫ Nn,m×N w(r, θ) rdr dθ = ∫ Pn,m Jn( αn,m a r)r dr ∫ P cos(nθ − δ) dθ + ∫ Nn,m Jn( αn,m a r)r dr ∫ N cos(nθ − δ) dθ = Jn,m , and similarly∫ w<0 w(r, θ)	cache/ejde-599.pdf	txt/ejde-599.txt