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1: 5.21 Methods of Computation
For the left half-plane we can continue the backward recurrence or make use of the reflection formula (5.5.3). …
2: About the Project
Figure 1: The Editors and 9 of the 10 Associate Editors of the DLMF Project (photo taken at 3rd Editors Meeting, April, 2001). The front row, from left to right: Ronald F. …The back row, from left to right: William P. …
3: 13.12 Products
4: 13.5 Continued Fractions
This continued fraction converges to the meromorphic function of z on the left-hand side everywhere in . … This continued fraction converges to the meromorphic function of z on the left-hand side throughout the sector | ph z | < π . …
5: 13.17 Continued Fractions
This continued fraction converges to the meromorphic function of z on the left-hand side for all z . … This continued fraction converges to the meromorphic function of z on the left-hand side throughout the sector | ph z | < π . …
6: Philip J. Davis
In 1957, Davis took over as Chief, Numerical Analysis Section when John Todd and his wife Olga Taussky-Todd, feeling a strong pull toward teaching and research, left to pursue full-time positions at the California Institute of Technology. … Davis left NBS in 1963 to become a faculty member in the Division of Applied Mathematics at Brown University, but during the early development of the DLMF, which started in 1998, he was invited back to give a talk and speak with DLMF project members about their plans. …
7: 5.10 Continued Fractions
5.10.1 Ln Γ ( z ) + z - ( z - 1 2 ) ln z - 1 2 ln ( 2 π ) = a 0 z + a 1 z + a 2 z + a 3 z + a 4 z + a 5 z + ,
8: 10.70 Zeros
In the case ν = 0 , numerical tabulations (Abramowitz and Stegun (1964, Table 9.12)) indicate that each of (10.70.2) corresponds to the m th zero of the function on the left-hand side. …
9: 19.10 Relations to Other Functions
In each case when y = 1 , the quantity multiplying R C supplies the asymptotic behavior of the left-hand side as the left-hand side tends to 0. …
10: 2.3 Integrals of a Real Variable
assume a and b are finite, and q ( t ) is infinitely differentiable on [ a , b ] . … provided that the integral on the left-hand side of (2.3.9) converges for all sufficiently large values of x . … Without loss of generality, we assume that this minimum is at the left endpoint a . … When the parameter x is large the contributions from the real and imaginary parts of the integrand in … For the more general integral (2.3.19) we assume, without loss of generality, that the stationary point (if any) is at the left endpoint. …