Problem #84

It is well-known that the infinite series a(x) = 1 + x²/2! + x⁴/4! + ... and b(x) = x + x³/3! + x⁵/5! + ... satisfy the relations

a(x)² - b(x)² = 1,
a(x + y) = a(x)a(y) + b(x)b(y)
b(x + y) = a(x)b(y) + b(x)a(y)

[Note: a(x) = cosh(x) and b(x) = sinh(x).]

Let

u(x) = 1 + x³/3! + x⁶/6! + x⁹/9! + ...,

v(x) = x + x⁴/4! + x⁷/7! + x¹⁰/10! + ..., and

w(x) = x²/2! + x⁵/5! + x⁸/8! + x¹¹/11! + ...