About the Project
NIST

elementary identities

AdvancedHelp

(0.001 seconds)

1—10 of 14 matching pages

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
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: 25.5 Integral Representations
    §25.5(i) In Terms of Elementary Functions
    25.5.6 ζ ( s ) = 1 2 + 1 s - 1 + 1 Γ ( s ) 0 ( 1 e x - 1 - 1 x + 1 2 ) x s - 1 e x d x , s > - 1 .
    25.5.14 ω ( x ) n = 1 e - n 2 π x = 1 2 ( θ 3 ( 0 | i x ) - 1 ) .
    7: 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 .
    These approximations are in terms of elementary functions. …
    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: 1.18 Linear 2nd Order Differential Operators and Eigenfunction Expansions
    §1.18(iv) Discrete Eigenfunction Expansions, Convergence, Parseval’s Identity
    Parseval’s identity and Bessel’s Inequality
    Resolution of the Identity, Completeness, and Spectral Expansions for a Discrete Spectrum
    §1.18(v) A Continuous Spectrum of Eigenvalues: Normalization, Resolution of the Identity, and Spectral Expansions
    See Friedman (1990, pages 233 – 252) for elementary discussions of both equations; also the references in §1.18(vii).