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31—36 of 36 matching pages

31: Errata
  • Section 19.25(vi)

    This subsection has been significantly updated. In particular, the following formulae have been corrected. Equation (19.25.35) has been replaced by

    19.25.35 z + 2 ω = ± R F ( ( z ) - e 1 , ( z ) - e 2 , ( z ) - e 3 ) ,

    in which the left-hand side z has been replaced by z + 2 ω for some 2 ω 𝕃 , and the right-hand side has been multiplied by ± 1 . Equation (19.25.37) has been replaced by

    19.25.37 ζ ( z + 2 ω ) + ( z + 2 ω ) ( z ) = ± 2 R G ( ( z ) - e 1 , ( z ) - e 2 , ( z ) - e 3 ) ,

    in which the left-hand side ζ ( z ) + z ( z ) has been replaced by ζ ( z + 2 ω ) + ( z + 2 ω ) ( z ) and the right-hand side has been multiplied by ± 1 . Equation (19.25.39) has been replaced by

    19.25.39 ζ ( ω j ) + ω j e j = 2 R G ( 0 , e j - e k , e j - e ) ,

    in which the left-hand side η j was replaced by ζ ( ω j ) , for some 2 ω j 𝕃 and ( ω j ) = e j . Equation (19.25.40) has been replaced by

    19.25.40 z + 2 ω = ± σ ( z ) R F ( σ 1 2 ( z ) , σ 2 2 ( z ) , σ 3 2 ( z ) ) ,

    in which the left-hand side z has been replaced by z + 2 ω , and the right-hand side was multiplied by ± 1 . For more details see §19.25(vi).

  • Equation (23.12.2)
    23.12.2 ζ ( z ) = π 2 4 ω 1 2 ( z 3 + 2 ω 1 π cot ( π z 2 ω 1 ) - 8 ( z - ω 1 π sin ( π z ω 1 ) ) q 2 + O ( q 4 ) )

    Originally, the factor of 2 was missing from the denominator of the argument of the cot function.

    Reported by Blagoje Oblak on 2019-05-27

  • Subsection 19.25(vi)

    The Weierstrass lattice roots e j , were linked inadvertently as the base of the natural logarithm. In order to resolve this inconsistency, the lattice roots e j , and lattice invariants g 2 , g 3 , now link to their respective definitions (see §§23.2(i), 23.3(i)).

    Reported by Felix Ospald.

  • Equation (19.25.37)

    The Weierstrass zeta function was incorrectly linked to the definition of the Riemann zeta function. However, to the eye, the function appeared correct. The link was corrected.

  • Equation (23.2.4)
    23.2.4 ( z ) = 1 z 2 + w 𝕃 { 0 } ( 1 ( z - w ) 2 - 1 w 2 )

    Originally the denominator ( z - w ) 2 was given incorrectly as ( z - w 2 ) .

    Reported 2012-02-16 by James D. Walker.

  • 32: 32.13 Reductions of Partial Differential Equations
    Depending whether A = 0 or A 0 , v ( z ) is expressible in terms of the Weierstrass elliptic function (§23.2) or solutions of P I , respectively. …
    33: 1.10 Functions of a Complex Variable
    M -test
    Weierstrass Product
    34: 20.11 Generalizations and Analogs
    As in §20.11(ii), the modulus k of elliptic integrals (§19.2(ii)), Jacobian elliptic functions (§22.2), and Weierstrass elliptic functions (§23.6(ii)) can be expanded in q -series via (20.9.1). …
    35: Software Index
    36: 1.9 Calculus of a Complex Variable
    Weierstrass M -test