zeros
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11: 14.27 Zeros
§14.27 Zeros
► (either side of the cut) has exactly one zero in the interval if either of the following sets of conditions holds: …For all other values of the parameters has no zeros in the interval . ►For complex zeros of see Hobson (1931, §§233, 234, and 238).12: 10.21 Zeros
§10.21 Zeros
… ► … ►§10.21(vi) McMahon’s Asymptotic Expansions for Large Zeros
… ► … ►The zeros of the functions …13: 10.70 Zeros
§10.70 Zeros
►Asymptotic approximations for large zeros are as follows. … ►
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►In the case , numerical tabulations (Abramowitz and Stegun (1964, Table 9.12)) indicate that each of (10.70.2) corresponds to the th zero of the function on the left-hand side.
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14: 28.9 Zeros
§28.9 Zeros
►For real each of the functions , , , and has exactly zeros in . …For the zeros of and approach asymptotically the zeros of , and the zeros of and approach asymptotically the zeros of . …Furthermore, for and also have purely imaginary zeros that correspond uniquely to the purely imaginary -zeros of (§10.21(i)), and they are asymptotically equal as and . There are no zeros within the strip other than those on the real and imaginary axes. …15: 7.13 Zeros
§7.13 Zeros
►§7.13(i) Zeros of
… ►§7.13(iii) Zeros of the Fresnel Integrals
… ►§7.13(iv) Zeros of
… ►16: 36.7 Zeros
§36.7 Zeros
►§36.7(i) Fold Canonical Integral
… ► … ►All zeros have , and fall into two classes. … ►The zeros are approximated by solutions of the equation …17: 25.18 Methods of Computation
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§25.18(i) Function Values and Derivatives
… ►§25.18(ii) Zeros
►Most numerical calculations of the Riemann zeta function are concerned with locating zeros of in an effort to prove or disprove the Riemann hypothesis, which states that all nontrivial zeros of lie on the critical line . Calculations to date (2008) have found no nontrivial zeros off the critical line. …18: 10.75 Tables
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