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V. A. Krechmar
V. A. Krechmar

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Article
  • Date submitted
    1928-09-30
  • Date accepted
    1928-11-10

Application of singular elliptic functions to the investigation of certain properties of Legendre polynomials

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In this work, the following theorem is proved. Let m be a negative integer containing no square divisors. Consider the quadratic field k(√m) and let ω1, ω2 be a basis of some ideal of this field, with the imaginary part of the ratio ω2/ω1 being positive. Furthermore, let ρ(u; ω1, ω2, ω3) be the well-known Weierstrass function (in what follows we will index the basis ω1, ω2 such that the ratio ω2/ω1 has a positive imaginary part), which satisfies the following differential equation

How to cite: Krechmar V.A. Application of singular elliptic functions to the investigation of certain properties of Legendre polynomials // Journal of Mining Institute. 1929. Vol. 7. Iss. 3. p. 69-81.