duplication%20formula
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1: 5.5 Functional Relations
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§5.5(ii) Reflection
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5.5.3
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§5.5(iii) Multiplication
►Duplication Formula
… ►Gauss’s Multiplication Formula
…2: 20.7 Identities
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§20.7(ii) Addition Formulas
… ►§20.7(iii) Duplication Formula
… ►§20.7(iv) Reduction Formulas for Products
… ►See Lawden (1989, pp. 19–20). … ►§20.7(ix) Addendum to 20.7(iv) Reduction Formulas for Products
…3: 10.60 Sums
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§10.60(ii) Duplication Formulas
…4: 20.11 Generalizations and Analogs
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►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.
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5: 19.11 Addition Theorems
6: 23.10 Addition Theorems and Other Identities
7: 19.36 Methods of Computation
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§19.36(i) Duplication Method
►Numerical differences between the variables of a symmetric integral can be reduced in magnitude by successive factors of 4 by repeated applications of the duplication theorem, as shown by (19.26.18). … ►The duplication method starts with computation of . …Alternatively, the first duplication is done analytically as in Carlson and FitzSimons (2000), where further information can be found. … ►Here is computed either by the duplication algorithm in Carlson (1995) or via (19.2.19). …8: 19.26 Addition Theorems
9: Gergő Nemes
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►As of September 20, 2021, Nemes performed a complete analysis and acted as main consultant for the update of the source citation and proof metadata for every formula in Chapter 25 Zeta and Related Functions.
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10: Wolter Groenevelt
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►As of September 20, 2022, Groenevelt performed a complete analysis and acted as main consultant for the update of the source citation and proof metadata for every formula in Chapter 18 Orthogonal Polynomials.
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