About the Project
NIST

as functions of parameters

AdvancedHelp

(0.013 seconds)

1—10 of 371 matching pages

1: 31.13 Asymptotic Approximations
§31.13 Asymptotic Approximations
2: 28.27 Addition Theorems
Addition theorems provide important connections between Mathieu functions with different parameters and in different coordinate systems. …
3: 28.21 Graphics
§28.21 Graphics
Radial Mathieu Functions: Surfaces
See accompanying text
Figure 28.21.6: Ms 1 ( 2 ) ( x , h ) for 0.2 h 2 , 0 x 2 . Magnify 3D Help
4: 8.17 Incomplete Beta Functions
8.17.4 I x ( a , b ) = 1 - I 1 - x ( b , a ) .
8.17.6 I x ( a , a ) = 1 2 I 4 x ( 1 - x ) ( a , 1 2 ) , 0 x 1 2 .
8.17.13 ( a + b ) I x ( a , b ) = a I x ( a + 1 , b ) + b I x ( a , b + 1 ) ,
8.17.20 I x ( a , b ) = I x ( a + 1 , b ) + x a ( x ) b a B ( a , b ) ,
8.17.21 I x ( a , b ) = I x ( a , b + 1 ) - x a ( x ) b b B ( a , b ) .
5: 16.22 Asymptotic Expansions
For asymptotic expansions of Meijer G -functions with large parameters see Fields (1973, 1983).
6: 33.13 Complex Variable and Parameters
§33.13 Complex Variable and Parameters
33.13.2 R = ( 2 + 1 ) C ( η ) / C - 1 ( η ) .
7: 33.22 Particle Scattering and Atomic and Molecular Spectra
k Scaling
Z Scaling
i k Scaling
§33.22(iii) Conversions Between Variables
§33.22(vii) Complex Variables and Parameters
8: 20.1 Special Notation
m , n

integers.

q ( )

the nome, q = e i π τ , 0 < | q | < 1 . Since τ is not a single-valued function of q , it is assumed that τ is known, even when q is specified. Most applications concern the rectangular case τ = 0 , τ > 0 , so that 0 < q < 1 and τ and q are uniquely related.

9: Bibliography U
  • F. Ursell (1984) Integrals with a large parameter: Legendre functions of large degree and fixed order. Math. Proc. Cambridge Philos. Soc. 95 (2), pp. 367–380.
  • 10: 31.1 Special Notation
    Sometimes the parameters are suppressed.