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math.FA2019★ 1 cited
Addition formulas of Leaf Functions and Hyperbolic Leaf Functions
Kazunori Shinohara
Addition formulas exist in trigonometric functions. Double-angle and half-angle formulas can be derived from these formulas. Moreover, the relation equation between the trigonometr…
math.FA2019★ 1 cited
Damped and Divergence Exact Solutions for the Duffing Equation using Leaf Functions and Hyperbolic Leaf Functions
Kazunori Shinohara
According to the wave power rule, the second derivative of a function with respect to the variable t is equal to negative n times the function raised to the power of 2n-1. Solving…
math.FA2017★ 7 cited
Addition Formulas of Leaf Functions According to Integral Root of Polynomial Based on Analogies of Inverse Trigonometric Functions and Inverse Lemniscate Functions
Kazunori Shinohara
The second derivative of a function r(t) with respect to a variable t is equal to -n times the function raised to the 2n-1 power of r(t); using this definition, an ordinary differe…