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

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