Weierstrass P-function
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11—20 of 38 matching pages
11: 23.1 Special Notation
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βΊ
βΊ
βΊThe main functions treated in this chapter are the Weierstrass
-function
; the Weierstrass zeta function
; the Weierstrass sigma function
; the elliptic modular function
; Klein’s complete invariant ; Dedekind’s eta function
.
…
lattice in . | |
… | |
nome. | |
discriminant . | |
… |
12: 23.6 Relations to Other Functions
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βΊ
§23.6(i) Theta Functions
… βΊ§23.6(ii) Jacobian Elliptic Functions
… βΊ§23.6(iii) General Elliptic Functions
… βΊ§23.6(iv) Elliptic Integrals
… βΊ13: 23.5 Special Lattices
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βΊ
§23.5(ii) Rectangular Lattice
… βΊIn this case the lattice roots , , and are real and distinct. … βΊ§23.5(iii) Lemniscatic Lattice
… βΊ§23.5(iv) Rhombic Lattice
… βΊ§23.5(v) Equianharmonic Lattice
…14: 23.11 Integral Representations
15: 14.27 Zeros
§14.27 Zeros
βΊ (either side of the cut) has exactly one zero in the interval if either of the following sets of conditions holds: …For all other values of the parameters has no zeros in the interval . βΊFor complex zeros of see Hobson (1931, §§233, 234, and 238).16: 23.19 Interrelations
17: 23.12 Asymptotic Approximations
18: 23.8 Trigonometric Series and Products
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βΊ
§23.8(i) Fourier Series
… βΊ§23.8(ii) Series of Cosecants and Cotangents
… βΊ
23.8.3
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βΊwhere in (23.8.4) the terms in and are to be bracketed together (the Eisenstein convention or principal value: see Weil (1999, p. 6) or Walker (1996, p. 3)).
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βΊ