n-tuple formulas
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21: Need Help?
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22: 5.21 Methods of Computation
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►For the left half-plane we can continue the backward recurrence or make use of the reflection formula (5.5.3).
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23: 12.16 Mathematical Applications
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►PCFs are also used in integral transforms with respect to the parameter, and inversion formulas exist for kernels containing PCFs.
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24: 30.10 Series and Integrals
25: 31.18 Methods of Computation
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►Subsequently, the coefficients in the necessary connection formulas can be calculated numerically by matching the values of solutions and their derivatives at suitably chosen values of ; see Laĭ (1994) and Lay et al. (1998).
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26: 25.10 Zeros
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§25.10(ii) Riemann–Siegel Formula
… ►Sign changes of are determined by multiplying (25.9.3) by to obtain the Riemann–Siegel formula: ►
25.10.3
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►Calculations based on the Riemann–Siegel formula reveal that the first ten billion zeros of in the critical strip are on the critical line (van de Lune et al. (1986)).
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27: 24.17 Mathematical Applications
28: 36.4 Bifurcation Sets
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§36.4(i) Formulas
… ► , cusp bifurcation set: … ► , swallowtail bifurcation set: … ►Elliptic umbilic bifurcation set (codimension three): for fixed , the section of the bifurcation set is a three-cusped astroid … ►Hyperbolic umbilic bifurcation set (codimension three): …29: 35.2 Laplace Transform
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Inversion Formula
…30: 24.5 Recurrence Relations
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