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1: 23.15 Definitions
23.15.5 f ( 𝒜 τ ) = c 𝒜 ( c τ + d ) f ( τ ) , τ > 0 ,
where c 𝒜 is a constant depending only on 𝒜 , and (the level) is an integer or half an odd integer. (Some references refer to 2 as the level). …
2: 23.18 Modular Transformations
and λ ( τ ) is a cusp form of level zero for the corresponding subgroup of SL ( 2 , ) . … J ( τ ) is a modular form of level zero for SL ( 2 , ) . … Note that η ( τ ) is of level 1 2 . …
3: 3.1 Arithmetics and Error Measures
§3.1(iv) Level-Index Arithmetic
In level-index arithmetic x is represented by + a (or - ( + a ) for negative numbers). … For further references on level-index arithmetic (and also other arithmetics) see Anuta et al. (1996). …
4: Mathematical Introduction
In the Handbook this information is grouped at the section level and appears under the heading Sources in the References section. In the DLMF this information is provided in pop-up windows at the subsection level. …
5: Bibliography T
  • C. A. Tracy and H. Widom (1994) Level-spacing distributions and the Airy kernel. Comm. Math. Phys. 159 (1), pp. 151–174.
  • 6: Bibliography C
  • C. W. Clenshaw, F. W. J. Olver, and P. R. Turner (1989) Level-Index Arithmetic: An Introductory Survey. In Numerical Analysis and Parallel Processing (Lancaster, 1987), P. R. Turner (Ed.), Lecture Notes in Math., Vol. 1397, pp. 95–168.
  • 7: Bibliography S
  • J. Shao and P. Hänggi (1998) Decoherent dynamics of a two-level system coupled to a sea of spins. Phys. Rev. Lett. 81 (26), pp. 5710–5713.
  • 8: 18.27 q -Hahn Class
    The generic (top level) cases are the q -Hahn polynomials and the big q -Jacobi polynomials, each of which depends on three further parameters. …