Opened 4 years ago

# implement integrals resulting in 2F1 and AppellF1 expressions

Reported by: Owned by: rws 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 4 years ago by rws

• Dependencies set to #22651

### comment:2 Changed 4 years ago by rws

• Description modified (diff)

### comment:3 Changed 4 years ago by rws

• Dependencies changed from #22651 to #22651, #22763
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