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1: 22.6 Elementary Identities
§22.6 Elementary Identities
See §22.17.
2: Guide to Searching the DLMF
Table 3: A sample of recognized symbols
Symbols Comments
-= For equivalence
All elementary functions Such as sin, cos, tan, Ln, log, exp
3: 18.9 Recurrence Relations and Derivatives
Identities similar to (18.9.11) and (18.9.12) involving W n ( x ) and T n ( x ) can be obtained using rows 4 and 7 in Table 18.6.1. …
4: Bibliography M
  • S. C. Milne (1985b) An elementary proof of the Macdonald identities for A l ( 1 ) . Adv. in Math. 57 (1), pp. 34–70.
  • 5: 17.17 Physical Applications
    In exactly solved models in statistical mechanics (Baxter (1981, 1982)) the methods and identities of §17.12 play a substantial role. … See Kassel (1995). …
    6: 35.7 Gaussian Hypergeometric Function of Matrix Argument
    35.7.2 P ν ( γ , δ ) ( 𝐓 ) = Γ m ( γ + ν + 1 2 ( m + 1 ) ) Γ m ( γ + 1 2 ( m + 1 ) ) F 1 2 ( ν , γ + δ + ν + 1 2 ( m + 1 ) γ + 1 2 ( m + 1 ) ; 𝐓 ) , 𝟎 < 𝐓 < 𝐈 ; γ , δ , ν ; ( γ ) > 1 .
    35.7.7 F 1 2 ( a , b c ; 𝐈 ) = Γ m ( c ) Γ m ( c a b ) Γ m ( c a ) Γ m ( c b ) , ( c ) , ( c a b ) > 1 2 ( m 1 ) .
    These approximations are in terms of elementary functions. …
    7: 18.39 Applications in the Physical Sciences
    18.39.22 T e 2 2 m 2 = 2 2 m 1 r 2 d d r r 2 d d r + L 2 2 m r 2 ,
    18.39.27 ( 2 2 m e 2 Z e 2 4 π ϵ 0 r ) Ψ ( r , θ , ϕ ) = E Ψ ( r , θ , ϕ ) .
    In what follows the radial and spherical radial eigenfunctions corresponding to (18.39.27) are found in four different notations, with identical eigenvalues, all of which appear in the current and past mathematical and theoretical physics and chemistry literatures, regarding this central problem. … which corresponds to the exact results, in terms of Whittaker functions, of §§33.2 and 33.14, in the sense that projections onto the functions ϕ n , l ( s r ) / r , the functions bi-orthogonal to ϕ n , l ( s r ) , are identical. …
    8: Bibliography S
  • L. Shen (1998) On an identity of Ramanujan based on the hypergeometric series F 1 2 ( 1 3 , 2 3 ; 1 2 ; x ) . J. Number Theory 69 (2), pp. 125–134.
  • R. Sitaramachandrarao and B. Davis (1986) Some identities involving the Riemann zeta function. II. Indian J. Pure Appl. Math. 17 (10), pp. 1175–1186.
  • SLATEC (free Fortran library)
  • D. M. Smith (1989) Efficient multiple-precision evaluation of elementary functions. Math. Comp. 52 (185), pp. 131–134.
  • 9: Bibliography R
  • J. Riordan (1979) Combinatorial Identities. Robert E. Krieger Publishing Co., Huntington, NY.
  • M. D. Rogers (2005) Partial fractions expansions and identities for products of Bessel functions. J. Math. Phys. 46 (4), pp. 043509–1–043509–18.
  • K. H. Rosen (2004) Elementary Number Theory and its Applications. 5th edition, Addison-Wesley, Reading, MA.
  • 10: 3.1 Arithmetics and Error Measures
    3.1.3 N min 2 E min | x | 2 E max + 1 ( 1 2 p ) N max .
    The elementary arithmetical operations on intervals are defined as follows: … with x 0 and the unique nonnegative integer such that a ln ( x ) [ 0 , 1 ) . …