About the Project

cardinal function

AdvancedHelp

(0.001 seconds)

5 matching pages

1: 24.17 Mathematical Applications
►The members of 𝒮 n are called cardinal spline functions. The functions►
Bernoulli Monosplines
►A function of the form x n S ⁡ ( x ) , with S ⁡ ( x ) 𝒮 n 1 is called a cardinal monospline of degree n . …For each n = 1 , 2 , the function M n ⁡ ( x ) is also the unique cardinal monospline of degree n satisfying (24.17.6), provided that …
2: 3.3 Interpolation
►For interpolation of a bounded function f on ℝ the cardinal function of f is defined by ►
3.3.43 C ⁡ ( f , h ) ⁢ ( x ) = k = f ⁢ ( k ⁢ h ) ⁢ S ⁡ ( k , h ) ⁢ ( x ) ,
3: 26.1 Special Notation
►(For other notation see Notation for the Special Functions.) ► ►►►
x real variable.
| A | number of elements of a finite set A .
►The main functions treated in this chapter are: ► ►►►►
( m n ) binomial coefficient.
p ⁡ ( n ) number of partitions of n .
p k ⁡ ( n ) number of partitions of n into at most k parts.
4: Bibliography S
►
  • I. J. Schoenberg (1973) Cardinal Spline Interpolation. Society for Industrial and Applied Mathematics, Philadelphia, PA.
  • ►
  • J. Segura and A. Gil (1999) Evaluation of associated Legendre functions off the cut and parabolic cylinder functions. Electron. Trans. Numer. Anal. 9, pp. 137–146.
  • ►
  • H. Shanker (1939) On the expansion of the parabolic cylinder function in a series of the product of two parabolic cylinder functions. J. Indian Math. Soc. (N. S.) 3, pp. 226–230.
  • ►
  • C. L. Siegel (1973) Topics in Complex Function Theory. Vol. III: Abelian Functions and Modular Functions of Several Variables. Interscience Tracts in Pure and Applied Mathematics, No. 25, Wiley-Interscience, [John Wiley & Sons, Inc], New York-London-Sydney.
  • ►
  • I. A. Stegun and R. Zucker (1981) Automatic computing methods for special functions. IV. Complex error function, Fresnel integrals, and other related functions. J. Res. Nat. Bur. Standards 86 (6), pp. 661–686.
  • 5: 26.18 Counting Techniques
    ►
    26.18.1 | S ∖ ( A 1 A 2 ⋯ A n ) | = | S | + t = 1 n ( 1 ) t ⁢ 1 j 1 < j 2 < ⋯ < j t n | A j 1 A j 2 ⋯ A j t | .
    ►For further examples in the use of generating functions, see Stanley (1997, 1999) and Wilf (1994). …