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§20.11(i) Gauss Sum… ► … ►This is Jacobi’s inversion problem of §20.9(ii). … ►Such sets of twelve equations include derivatives, differential equations, bisection relations, duplication relations, addition formulas (including new ones for theta functions), and pseudo-addition formulas. …
The wording was changed to make the integration variable more apparent.
Additional keywords are being added to formulas (an ongoing project); these are visible in the associated ‘info boxes’ linked to the icons to the right of each formula, and provide better search capabilities.
The generalized hypergeometric function of matrix argument , was linked inadvertently as its single variable counterpart . Furthermore, the Jacobi function of matrix argument , and the Laguerre function of matrix argument , were also linked inadvertently (and incorrectly) in terms of the single variable counterparts given by , and . In order to resolve these inconsistencies, these functions now link correctly to their respective definitions.
Sentences were added specifying that some equations in these subsections require special care under certain circumstances. Also, (15.4.6) was expanded by adding the formula .
Report by Louis Klauder on 2017-01-01.
Special cases of normalization of Jacobi polynomials for which the general formula is undefined have been stated explicitly in Table 18.3.1.