Weierstrass’s
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11—20 of 23 matching pages
11: 25.1 Special Notation
12: 23.4 Graphics
§23.4(i) Real Variables
►Line graphs of the Weierstrass functions , , and , illustrating the lemniscatic and equianharmonic cases. … ► … ►§23.4(ii) Complex Variables
►Surfaces for the Weierstrass functions , , and . …13: William P. Reinhardt
14: 22.1 Special Notation
15: 20.9 Relations to Other Functions
§20.9(ii) Elliptic Functions and Modular Functions
►See §§22.2 and 23.6(i) for the relations of Jacobian and Weierstrass elliptic functions to theta functions. ►The relations (20.9.1) and (20.9.2) between and (or ) are solutions of Jacobi’s inversion problem; see Baker (1995) and Whittaker and Watson (1927, pp. 480–485). …16: 20.11 Generalizations and Analogs
§20.11(ii) Ramanujan’s Theta Function and -Series
… ►§20.11(iii) Ramanujan’s Change of Base
►As in §20.11(ii), the modulus of elliptic integrals (§19.2(ii)), Jacobian elliptic functions (§22.2), and Weierstrass elliptic functions (§23.6(ii)) can be expanded in -series via (20.9.1). …This is Jacobi’s inversion problem of §20.9(ii). …17: Errata
The title of the paragraph which was previously “Gasper’s -Analog of Clausen’s Formula” has been changed to “Gasper’s -Analog of Clausen’s Formula (16.12.2)”.
This subsection has been significantly updated. In particular, the following formulae have been corrected. Equation (19.25.35) has been replaced by
in which the left-hand side has been replaced by for some , and the right-hand side has been multiplied by . Equation (19.25.37) has been replaced by
in which the left-hand side has been replaced by and the right-hand side has been multiplied by . Equation (19.25.39) has been replaced by
in which the left-hand side was replaced by , for some and . Equation (19.25.40) has been replaced by
in which the left-hand side has been replaced by , and the right-hand side was multiplied by . For more details see §19.25(vi).
The Weierstrass lattice roots were linked inadvertently as the base of the natural logarithm. In order to resolve this inconsistency, the lattice roots , and lattice invariants , , now link to their respective definitions (see §§23.2(i), 23.3(i)).
Reported by Felix Ospald.
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.
Originally the denominator was given incorrectly as .
Reported 2012-02-16 by James D. Walker.