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Theta Functions   &   Elliptic Functions

(2016-12-01)   Prototypical Theta Function
The basic idea.

Theta functions

(2016-12-07)   Legendre form of elliptic ingegrals

Legendre forms of elliptic integrals

(2016-12-07)   Carlson's symmetric forms  (2004)
Canonical forms for elliptic integrals.

Carlson symmetric forms   |   Bille C. Carlson  (1924-2013; Ph.D. 1950).

(2016-15-05)   Abel Elliptic Functions
Functions with two periods.

Elliptic integrals (MathWorld)   |   Wikipedia

(2016-11-30)   Jacobi Theta Functions
Elliptic functions.

Notational variations   |   MathWorld :   Jacobi Theta Functions

(2016-12-01)   False Theta Functions   (L.J. Rogers,  1894, 1917)

False, Partial and Mock Theta Functions  Bringmann, Folsom, Rhoades  (2011-04-15)
Rogers-Ramanujan Identities (1894, 1913, Schur 1917)  |  Leonard J. Rogers (1862-1933)

(2016-12-02)   q-analogs

q-analog theory   |   MathWorld

(2016-12-02)   Ramanujan Theta Functions
Not to be confused with his later  mock theta functions.

Pochhammer's symbol   |   Ramanujan theta function

(2016-12-01)   Mock Theta Functions  (S. Ramanujan, 1920)
The major preoccupation of  Ramanujan in his last days.

Three months before he died,  Ramanujan  coined the term  mock theta functions  in his last letter  to  G.H. Hardy  (January 1920)  ntroducing  17  of them.  In his  lost notebook  (uncovered by George Andrews in 1976)  3  other such functions appear,  although not identified as such.

Reconstructing the discovery of the mock theta function (40:23)  by  George E. Andrews  (2021-03-12).

(2016-12-07)   Partial Theta Functions

A Unified Approach to Partial and Mock Theta Functions   Robert C. Rhoades  (2011)