OFFSET
0,3
COMMENTS
On pages 635 to 637 of the Handbook, T(m, n) is denoted by a_{m, n}. Equation 18.5.6 is sigma(z) = Sum_{m, n>=0} a_{m, n} (1/2 g_2)^m (2 g_3)^n * z^(4m+6n+1) / (4m+6n+1)!. - Michael Somos, Sep 24 2021
REFERENCES
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 637.
LINKS
Nathaniel Johnston, Table of n, a(n) for n = 0..1325
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy]. See Table on p. 637.
Eric Weisstein's World of Mathematics, Weierstrass Sigma Function
FORMULA
T(0,0)=1, T(m,n)=0 if either m or n is negative; otherwise T(m,n)=3*(m+1)*T(m+1,n-1)+(16/3)*(n+1)*T(m-2,n+1)-(1/3)*(2*m+3*n-1)*(4*m+6*n-1)*T(m-1,n). [Abramowitz-Stegun, Eq. (18.5.8)].
EXAMPLE
Array begins:
1 -3 -54 14904 ...
-1 -18 4968 502200 ...
-9 513 257580 162100440 ...
69 33588 20019960 -9465715080 ...
321 2808945 -376375410 -4582619446320 ...
160839 -41843142 -210469286736 -1028311276281264 ...
...
CROSSREFS
KEYWORD
AUTHOR
N. J. A. Sloane, Apr 10 2011
EXTENSIONS
a(14)-a(29) from Nathaniel Johnston, Apr 11 2011
STATUS
approved