Opened 6 years ago

Last modified 6 years ago

#22650 new enhancement

implement integrals resulting in 2F1 and AppellF1 expressions

Reported by: Ralf Stephan 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: #22651, #22763 Stopgaps:

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Description (last modified by Ralf Stephan)

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 1.1.3.H
  • (bx)m(c+dx)n(e+fx)p, m,n not in ZZ --> Rules 1.1.3.A.1.*
  • (a+bx)m(c+dx)n(e+fx)p, m,n not in ZZ --> Rules 1.1.3.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
  • (cx)m(a+bxn)p, p not in ZZ --> Rules
  • (a+bxn)p(c+dxn)q, n(p+q+1)+1==0 --> Rule
  • (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

Change History (3)

comment:1 Changed 6 years ago by Ralf Stephan

Dependencies: #22651

comment:2 Changed 6 years ago by Ralf Stephan

Description: modified (diff)

comment:3 Changed 6 years ago by Ralf Stephan

Dependencies: #22651#22651, #22763
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