About the Project
NIST

Legendre relation

AdvancedHelp

(0.002 seconds)

11—20 of 64 matching pages

11: 18.9 Recurrence Relations and Derivatives
Table 18.9.1: Classical OP’s: recurrence relations (18.9.1).
p n ( x ) A n B n C n
12: 14.10 Recurrence Relations and Derivatives
§14.10 Recurrence Relations and Derivatives
13: Bibliography D
  • P. L. Duren (1991) The Legendre Relation for Elliptic Integrals. In Paul Halmos: Celebrating 50 Years of Mathematics, J. H. Ewing and F. W. Gehring (Eds.), pp. 305–315.
  • 14: 19.5 Maclaurin and Related Expansions
    §19.5 Maclaurin and Related Expansions
    15: 15.9 Relations to Other Functions
    Legendre
    §15.9(iv) Associated Legendre Functions; Ferrers Functions
    16: 14.21 Definitions and Basic Properties
    §14.21(iii) Properties
    17: 22.16 Related Functions
    Relation to Elliptic Integrals
    Relation to the Elliptic Integral E ( ϕ , k )
    Definition
    18: 19.6 Special Cases
    19: 19.21 Connection Formulas
    Legendre’s relation (19.7.1) can be written … If 0 < p < z and y = z + 1 , then as p 0 (19.21.6) reduces to Legendre’s relation (19.21.1). …
    20: 14.5 Special Values
    §14.5(v) μ = 0 , ν = ± 1 2