{"history":[],"article":{"id":"145673e3-e711-438e-835a-96e0c6f90383","title":"Nome (mathematics)","slug":"nome-mathematics","content":":::summary\n:::\n\n# \nIn [mathematics](https://bliptext.com/articles/mathematics), specifically the theory of [elliptic functions](https://bliptext.com/articles/elliptic-functions), the **nome** is a [special function](https://bliptext.com/articles/special-function) that belongs to the non-elementary functions.\nThis function is of great importance in the description of the elliptic functions, especially in the description of the modular identity of the [Jacobi theta function](https://bliptext.com/articles/theta-function), the [Hermite elliptic transcendents](https://bliptext.com/articles/bring-radical) and the [Weber modular functions](https://bliptext.com/articles/weber-modular-functions), that are used for solving equations of higher degrees.\n\n# Definition\nThe nome function is given by\nwhere K and iK' are the [quarter periods](https://bliptext.com/articles/quarter-period), and \\omega_1 and \\omega_2 are the [fundamental pair of periods](https://bliptext.com/articles/fundamental-pair-of-periods), and is the [half-period ratio](https://bliptext.com/articles/half-period-ratio).\nThe nome can be taken to be a function of any one of these quantities; conversely, any one of these quantities can be taken as functions of the nome.\nEach of them uniquely determines the others when 0

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