Opened 6 years ago

# implement integrals resulting in 2F1 and AppellF1 expressions

Reported by: Owned by: Ralf Stephan major sage-8.0 calculus N/A #22651, #22763

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 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

### 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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