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1: 28.22 Connection Formulas
The joining factors in the above formulas are given by
28.22.5 g e , 2 m ( h ) = ( 1 ) m 2 π ce 2 m ( 1 2 π , h 2 ) A 0 2 m ( h 2 ) ,
28.22.9 f e , m ( h ) = π / 2 g e , m ( h ) Mc m ( 2 ) ( 0 , h ) ,
28.22.10 f o , m ( h ) = π / 2 g o , m ( h ) Ms m ( 2 ) ( 0 , h ) ,
ge m ( 0 , h 2 ) = 1 2 π S m ( h 2 ) ( g o , m ( h ) ) 2 se m ( 0 , h 2 ) .
2: 28.1 Special Notation
The notation for the joining factors is …
f o , n ( h ) .
3: 28.35 Tables
  • National Bureau of Standards (1967) includes the eigenvalues a n ( q ) , b n ( q ) for n = 0 ( 1 ) 3 with q = 0 ( .2 ) 20 ( .5 ) 37 ( 1 ) 100 , and n = 4 ( 1 ) 15 with q = 0 ( 2 ) 100 ; Fourier coefficients for ce n ( x , q ) and se n ( x , q ) for n = 0 ( 1 ) 15 , n = 1 ( 1 ) 15 , respectively, and various values of q in the interval [ 0 , 100 ] ; joining factors g e , n ( q ) , f e , n ( q ) for n = 0 ( 1 ) 15 with q = 0 ( .5  to  10 ) 100 (but in a different notation). Also, eigenvalues for large values of q . Precision is generally 8D.

  • 4: Bibliography N
  • National Bureau of Standards (1967) Tables Relating to Mathieu Functions: Characteristic Values, Coefficients, and Joining Factors. 2nd edition, National Bureau of Standards Applied Mathematics Series, U.S. Government Printing Office, Washington, D.C..
  • 5: 23.20 Mathematical Applications
    The addition law states that to find the sum of two points, take the third intersection with C of the chord joining them (or the tangent if they coincide); then its reflection in the x -axis gives the required sum. …
    §23.20(iii) Factorization
    §27.16 describes the use of primality testing and factorization in cryptography. …