Opened 5 years ago

Last modified 5 years ago

#22650 new enhancement

implement integrals resulting in 2F1 and AppellF1 expressions — at Initial Version

Reported by: rws Owned by:
Priority: major Milestone: sage-8.0
Component: calculus Keywords:
Cc: Merged in:
Authors: Reviewers:
Report Upstream: N/A Work issues:
Branch: Commit:
Dependencies: Stopgaps:

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Description

These are the rules in the Rubi integrator's chapters 1.1, 1.2, and 1.3 that result in hypergeometric or AppellF1 expressions. They could be implemented to increase coverage of the available integration libraries:

  • (c+dx)n/(a+bx), n not in ZZ --> Rule 1.1.2.H.4
  • (bx)m(c+dx)n, --> Rules 1.1.2.H.1.*
  • (a+bx)m(c+dx)n --> Rules 1.1.2.H.2.*
  • (a+bx)m(c+dx)n(e+fx)p, m+n+p+2==0 --> Rules 1.3.1.H
  • (bx)m(c+dx)n(e+fx)p, m,n not in ZZ --> Rules 1.3.1.A.1.*
  • (a+bx)m(c+dx)n(e+fx)p, m,n not in ZZ --> Rules 1.3.1.A.2/3.*
  • (a+bx+cx2)p, 4p not in ZZ --> Rule 1.2.1.H
  • (a+bxn)p, p not in ZZ, a>0 --> Rule 1.3.1.7
  • (cx)m(a+bxn)p, p not in ZZ --> Rules 1.3.2.12
  • (a+bxn)p(c+dxn)q, n(p+q+1)+1==0 --> Rule 1.3.3.5.4
  • (ex)m(a+bxn)p(c+dxn)q, a,c>0, m!=1, m+n!=1 --> Rule 1.3.4.A.1
  • (axj+bxn)p, p not in ZZ, j!=n --> Rules 1.3.8.x
  • xm(axj+bxn)p, j!=n --> Rules 1.3.9.x

This could be useful even without a full #22410

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