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41: 20.7 Identities
The symmetry, applicable also to §§20.7(iii) and 20.7(vii), is obtained by modifying traditional theta functions in the manner recommended by Carlson (2011) and used for further purposes by Fukushima (2012). …
42: Bibliography S
  • P. Sarnak (1999) Quantum Chaos, Symmetry and Zeta Functions. Lecture I, Quantum Chaos. In Current Developments in Mathematics, 1997 (Cambridge, MA), R. Bott (Ed.), pp. 127–144.
  • 43: 2.3 Integrals of a Real Variable
    However, cancellation does not take place near the endpoints, owing to lack of symmetry, nor in the neighborhoods of zeros of p ( t ) because p ( t ) changes relatively slowly at these stationary points. …
    44: 18.5 Explicit Representations
    and two similar formulas by symmetry; compare the second row in Table 18.6.1. …
    45: 18.9 Recurrence Relations and Derivatives
    and a similar pair to (18.9.5) and (18.9.6) by symmetry; compare the second row in Table 18.6.1. …
    46: 18.15 Asymptotic Approximations
    By using the symmetry property given in the second row of Table 18.6.1, the roles of α and β can be interchanged. …
    47: 18.35 Pollaczek Polynomials
    There is the symmetry
    48: Bibliography K
  • T. H. Koornwinder (2015) Fractional integral and generalized Stieltjes transforms for hypergeometric functions as transmutation operators. SIGMA Symmetry Integrability Geom. Methods Appl. 11, pp. Paper 074, 22.
  • 49: 18.17 Integrals
    and three formulas similar to (18.17.9)–(18.17.11) by symmetry; compare the second row in Table 18.6.1. …
    50: 18.18 Sums
    and a similar pair of equations by symmetry; compare the second row in Table 18.6.1. …