Bailey pair and lemma

examples

• Conjugate Bailey pair (\(x=q,y\to\infty, z\to\infty\))
  \(\delta_n=q^{n^2}\)
  \(\gamma_n=\frac{q^{n^2}}{(q)_{\infty}}\)
  
• we get the Rogers-Ramanujan identity(Slater 18)
  \(\sum_{n=0}^{\infty}\frac{q^{n^2}}{ (q)_{n}}=\frac{(q^{3};q^{5})_{\infty}(q^{2};q^{5})_{\infty}(q^{5};q^{5})_{\infty}}{(q)_{\infty}}=\frac{1}{(q^{1};q^{5})_{\infty}(q^{4};q^{5})_{\infty}}\)
  

 

 

Bailey chain

• Bailey chain
  

 

 

related items

• Bloch group
  
• Bloch group, K-theory and dilogarithm
  
• manufacturing matrices from lower ranks
  
• q-analogue of summation formulas
  
• Rogers-Ramanujan continued fraction
  

 

 

articles

•  
  A. Schilling, S.O. Warnaar A generalization of the q-Saalschutz sum and the Burge transform, 2009
  
• Rogers-Ramanujan-Slater Type identities
  
  • Mc Laughlin, 2008
    
• Andrews–Gordon type identities from combinations of Virasoro characters
  
  • Boris Feigin, Omar Foda, Trevor Welsh, 2007
    
• Finite Rogers-Ramanujan Type Identities
  
  • Andrew V. Sills, 2003
    
• Virasoro character identities from the Andrews–Bailey construction
  
  • Foda, O., Quano, Y.-H, Int. J. Mod. Phys. A 12, 1651–1675 (1997)
    

• Multiple series Rogers-Ramanujan type identities.
  
  • George E. Andrews, Pacific J. Math.  Volume 114, Number 2 (1984), 267-283.
    
• Special values of the dilogarithm function
  
  • J. H. Loxton, 1984
• Wilfrid Norman Bailey
  
  • Slater, L. J. (1962), Journal of the London Mathematical Society. Second Series 37: 504–512
    
• Further identities of the Rogers-Ramanujan type
  
  • Slater, L. J. (1952),  Proceedings of the London Mathematical Society. Second Series 54: 147–167
    
• A New Proof of Rogers's Transformations of Infinite Series
  
  • Slater, L. J. (1952), Proc. London Math. Soc. 1951 s2-53: 460-475
    
• Identities of Rogers-Ramanujan type
  
  • Bailey, 1944