We first deduce a uniform formula forthe Fermi energy of degenerate and relativistic electrons in the weak-magnetic field approximation. Then we obtain an expression of the special solution for the electron Fermi energy through this formula, and express the electron Fermi energy as a function of electron fraction and matter density. Our method is universally suitable for relativistic electron- matter regions in neutron stars in the weak-magnetic field approximation.

ABSTRACT
1. INTRODUCTION
2. DEDUCTIONS OF FORMULAE
    2.1. Applications of Special Solution
3. SUMMARY
REFERENCES

• Zhi Fu Gao(Xinjiang Astronomical Observatory/Key Laboratory of Radio Astronomy, CAS, Nanjing)
• X. D. Li(Shchool of Astronomy and Space Science, Nanjing University)
• N. Wang(Xinjiang Astronomical Observatory)
• Q. H. Peng(Shchool of Astronomy and Space Science, Nanjing University)