Derivation of The 7D Polynomial from the Rydberg Equation

$R_H\equiv{m_ee^4\over8\epsilon_0^2h^3c}$

$1\equiv{m_ee^4\over8\epsilon_0^2h^3cR_H}$

$m_r={m_1m_2\over m_1+m_2}$

$m_1=m_p$

$m_2=m_e$

$m_r\approx m_e$

$1\equiv m_r{e^4\over8\epsilon_0^2h^3cR_H}$

$1\equiv{m_pm_e\over\left(m_p+m_e\right)}{e^4\over{8\epsilon_0^2h^3cR_H}}$

$1+{m_e\over m_p}\equiv{m_ee^4\over{8\epsilon_0^2h^3cR_H}}$

${\mu=\beta={m_p\over m_e}}={\alpha^2\over\pi r_pR_H}$

${1\over m_p}={\pi r_pc\over2h}$

$1\equiv{m_ee^4\over{8\epsilon_0^2h^3cR_H}}-{\pi r_pcm_e\over2h}$