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1: 14.7 Integer Degree and Order
§14.7(ii) Rodrigues-Type Formulas
§14.7(iii) Reflection Formulas
2: Gergő Nemes
As of September 20, 2021, Nemes performed a complete analysis and acted as main consultant for the update of the source citation and proof metadata for every formula in Chapter 25 Zeta and Related Functions. …
3: Wolter Groenevelt
As of September 20, 2022, Groenevelt performed a complete analysis and acted as main consultant for the update of the source citation and proof metadata for every formula in Chapter 18 Orthogonal Polynomials. …
4: 20 Theta Functions
Chapter 20 Theta Functions
5: Foreword
In 1964 the National Institute of Standards and Technology11 1 Then known as the National Bureau of Standards. published the Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, edited by Milton Abramowitz and Irene A. … November 20, 2009 …
6: 36.4 Bifurcation Sets
§36.4(i) Formulas
K = 2 , cusp bifurcation set: … K = 3 , swallowtail bifurcation set: … Elliptic umbilic bifurcation set (codimension three): for fixed z , the section of the bifurcation set is a three-cusped astroid … Hyperbolic umbilic bifurcation set (codimension three): …
7: 3.4 Differentiation
Two-Point Formula
Three-Point Formula
Four-Point Formula
Five-Point Formula
Six-Point Formula
8: 36.5 Stokes Sets
§36.5(ii) Cuspoids
36.5.4 80 x 5 40 x 4 55 x 3 + 5 x 2 + 20 x 1 = 0 ,
36.5.7 X = 9 20 + 20 u 4 Y 2 20 u 2 + 6 u 2 sign ( z ) ,
§36.5(iii) Umbilics
9: Bibliography N
  • D. Naylor (1984) On simplified asymptotic formulas for a class of Mathieu functions. SIAM J. Math. Anal. 15 (6), pp. 1205–1213.
  • D. Naylor (1987) On a simplified asymptotic formula for the Mathieu function of the third kind. SIAM J. Math. Anal. 18 (6), pp. 1616–1629.
  • D. Naylor (1989) On an integral transform involving a class of Mathieu functions. SIAM J. Math. Anal. 20 (6), pp. 1500–1513.
  • W. J. Nellis and B. C. Carlson (1966) Reduction and evaluation of elliptic integrals. Math. Comp. 20 (94), pp. 223–231.
  • E. W. Ng and M. Geller (1969) A table of integrals of the error functions. J. Res. Nat. Bur. Standards Sect B. 73B, pp. 1–20.
  • 10: 25.12 Polylogarithms
    25.12.3 Li 2 ( z ) + Li 2 ( z z 1 ) = 1 2 ( ln ( 1 z ) ) 2 , z [ 1 , ) .
    25.12.4 Li 2 ( z ) + Li 2 ( 1 z ) = 1 6 π 2 1 2 ( ln ( z ) ) 2 , z [ 0 , ) .
    25.12.6 Li 2 ( x ) + Li 2 ( 1 x ) = 1 6 π 2 ( ln x ) ln ( 1 x ) , 0 < x < 1 .
    See accompanying text
    Figure 25.12.1: Dilogarithm function Li 2 ( x ) , 20 x < 1 . Magnify
    See accompanying text
    Figure 25.12.2: Absolute value of the dilogarithm function | Li 2 ( x + i y ) | , 20 x 20 , 20 y 20 . … Magnify 3D Help