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  1. (b-a)2F1+a2F1(a+1)-b2F1(b+1)=0
  2. (c-2a-(b-a)z)2F1+a(1-z)2F1(a+1)-(c-a)2F1(a-1)=0
  3. (c-a-1)2F1+a2F1(a+1)-(c-1)2F1(c-1)=0
  4. (c-a-b)2F1+a(1-z)2F1(a+1)-(c-b)2F1(b-1)=0
  5. (c-a-b)2F1-(c-a)2F1(a-1)+b(1-z)2F1(b+1)=0
  6. (n+1)L (n+1)(x) = (2n+1-x)L n(x)-nL (n-1)(x)
  7. (n+2)C (n+2)^(lambda)(x)=2(lambda+n+1)xC (n+1)^(lambda)(x)-(2lambda+n)C n^(lambda)(x)
  8. (n+2lambda)C n^(lambda)(x)=2lambda(C n^(lambda+1)(x)-xC (n-1)^(lambda+1)(x))
  9. (z/(1-q))2Phi1(q,q;q^2;z)=Sum z^k/(1-q^k)
  10. *-c functions footer
  11. *-integral functions footer
  12. -log(1-x) less than x/(1-x)
  13. 0!=1
  14. 0F0(;;z)=exp(z)
  15. 0F1(;r;z)0F1(;r;-z)=0F3(r,r/2,r/2+1/2;-z^2/4)
  16. 0F1(;r;z)0F1(;s;z)=2F1(r/2+s/2, r/2+s/2-1/2;r,s,r+s-1;4z)
  17. 1+x greater than exp(x/(1+x)) for nonzero real x greater than -1
  18. 1/B(n,m)=m((n+m-1) choose (n-1))
  19. 1/B(n,m)=n((n+m-1) choose (m-1))
  20. 1/q-number as a q-number
  21. 1F1(a;2a;z)1F1(b;2b;-z)=2F3(a/2+b/2,a/2+b/2+1/2;a+1/2,b+1/2,a+b;z^2/4)
  22. 1F1(a;r;z)1F1(a;r;-z)=2F3(a,r-a;r,r/2,r/2+1/2;z^2/4)
  23. 1Phi0(a;;z)1Phi0(b;;az)=1Phi0(ab;;z)
  24. 1Phi0(a;;z) as infinite product
  25. 2F0(a,b;;z)2F0(a,b;;-z)=4F1(a,b,a/2+b/2,a/2+b/2+1/2;a+b;4z^2)
  26. 2F1(1,1;2;z)=-log(1-z)/z
  27. 2F1(1/2,1/2;3/2;z^2)=arcsin(z)/z
  28. 2F1(1/2,1;3/2;-z^2)=arctan(z)/z
  29. 2F1(1/2,1;3/2;z^2)=log((1+z)/(1-z))/(2z)
  30. 2F1(a,b;a+b+1/2;z)^2=3F2(2a,a+b,2b;a+b+1/2,2a+2b;z)
  31. 2Phi1(q,-1;-q;z)=1+2Sum z^k/(1+q^k)
  32. 2cos(mt)cos(nt)=cos((m+n)t)+cos((m-n)t)
  33. Abel p
  34. Abs(e^z-1) less than or equal to e^(abs(z))-1 less than or equal to abs(z)e^(abs(z))
  35. Abs(log(1+z)) less than or equal to -log(1-abs(z))
  36. Abs(log(1-x)) less than 3x/2
  37. Abs(z)/4 less than abs(e^z-1) less than (7abs(z))/4 for 0 less than abs(z) less than 1
  38. Absolute convergence of secant zeta function
  39. Airy Ai
  40. Airy Bi
  41. Airy functions footer
  42. Airy zeta function
  43. Airy zeta function at 2
  44. Alexander operator
  45. Algebraic number
  46. Alternating sum over bottom of binomial coefficient with top fixed equals 0
  47. Anger derivative recurrence
  48. Anger function
  49. Anger of integer order is Bessel J
  50. Anger three-term recurrence

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