It is well-known that the infinite series a(x) = 1 + x^{2}/2! + x^{4}/4! + ... and b(x) = x + x^{3}/3! + x^{5}/5! + ... satisfy the relations
[Note: a(x) = cosh(x) and b(x) = sinh(x).]
Let
v(x) = x + x^{4}/4! + x^{7}/7! + x^{10}/10! + ..., and
w(x) = x^{2}/2! + x^{5}/5! + x^{8}/8! + x^{11}/11! + ...