Abstract:
k=1 sin(2kθ)q k k(1 + q k + q 2k) occurs in one of Ramanujan’s inversion formulas for elliptic integrals. In this article, a common generalization of the cubic elliptic functions g1(θ; q) = 1
Citations
|
102
|
Special Functions
– Andrews, Askey, et al.
- 1999
|
|
71
|
Ramanujan’s Notebooks, Part V
– Berndt
- 1998
|
|
34
|
Collected Papers
– Ramanujan
- 1962
|
|
29
|
Elliptic Curves
– Knapp
- 1992
|
|
19
|
A cubic counterpart of Jacobi’s identity
– Borwein, Borwein
- 1991
|
|
19
|
Elliptic Functions
– Chandrasekharan
- 1985
|
|
18
|
Ramanujan’s theories of elliptic functions to alternative bases
– Berndt, Bhargava, et al.
- 1995
|
|
14
|
Some cubic modular identities
– Borwein, Borwein, et al.
- 1994
|
|
13
|
Cubic analogues of the Jacobian theta function θ(z, q
– Hirschhorn, Garvan, et al.
- 1993
|
|
13
|
Modular Functions in Analytic Number Theory
– Knopp
- 1970
|
|
11
|
On certain arithmetical functions, Trans
– Ramanujan
- 1916
|
|
4
|
Development of Elliptic Functions According to Ramanujan
– Venkatachaliengar
- 1988
|
|
4
|
A course of modern analysis, Reprint of the fourth
– Whittaker, Watson
- 1927
|
|
3
|
On sums of an even number of squares, and an even number of triangular numbers: an elementary approach based on Ramanujan’s 1ψ1 summation formula
– Cooper
- 2001
|
|
2
|
The development of elliptic functions according to Ramanujan and Venkatachaliengar
– Cooper
- 2001
|
|
1
|
Analogues of Jacobi’s inversion formula for the incomplete elliptic integral of the first kind
– Chan, Liu
- 2003
|
|
1
|
Cubic theta functions
– Cooper
|
|
1
|
Some Eisenstein series identities associated with the Borwein functions, Symbolic computation, number theory, special functions, physics and combinatorics
– Liu
- 1999
|
|
1
|
elliptic functions 59
– Ramanujan, Notebooks
- 1957
|