A Dictionary of Real Numbers by Jonathan Borwein

By Jonathan Borwein

How can we realize that the quantity . 93371663 . . . is basically 2 IoglQ(e + 7r)/2 ? Gauss saw that the number one. 85407467 . . . is (essentially) a rational price of an elliptic integral-an statement that used to be serious within the improvement of 19th century research. How can we come to a decision that this type of quantity is de facto a distinct worth of a well-known functionality with no the instruments Gauss had at his disposal, which have been, possibly, extra special perception and a prodigious reminiscence? a part of the reply, we are hoping, lies during this quantity. This ebook is established like a opposite phone book, or extra effectively, like a opposite instruction manual of distinctive functionality values. it's a record of simply over 100,000 eight-digit genuine numbers within the period [0,1) that come up because the first 8 digits of exact values of wide-spread features. it truly is designed for individuals, like ourselves, who come across a number of numbers computationally and wish to grasp if those numbers have a few easy shape. this isn't a very well-defined endeavor-every eight-digit quantity is rational and this isn't attention-grabbing. even if, the probabilities of an 8 digit quantity agreeing with a small rational, say with numerator and denominator under twenty-five, is small. therefore the checklist is comprised essentially of precise functionality reviews at quite a few algebraic and straightforward transcendental values. the precise numbers incorporated are defined under. every one access comprises the 1st 8 digits after the decimal aspect of the quantity in question.

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Extra resources for A Dictionary of Real Numbers

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5/2 0444 3125 II! /3/3 04899751 IJ! /3/4 04903883 In( y'2) - exp(1/3) 0490 4339 IJ! /3/2)-1/3 0491 1972 IJ! /3 + 3v'5/4 0492 1818 2X : In 2/10 04923355 sr : /2/4 + 4/5 0492 3431 eu : In(ln 2) 0492 4623 J 1 : In(e/3) 0492 5509 rt : (9,1,-6,3) 0492 5801 Ei : 9/25 0492 5924 eu : e/3 - 37r / 4 0492 6062 rt : (8,2,-9,-2) 0492 7853 lOX : P42 04928002 er : 51n 2/3 04930614 In : (e/3)1/2 0493 0700 J2 : 2/5/7 0493 2594 sr : 1O~/3 04934417 (: (5/3)3 0493 4783 Ei : 2~/7 04935475 at : 1/4 + 2/5/3 0493 6777 rt : (9,2,-4,4) 0493 7336 rt : (8,1,-7,-3) 0493 8271 sq : 2/9 0493 8728 rt : (6,6,-9,8) 04938948 IJ!

3/4 04903883 In( y'2) - exp(1/3) 0490 4339 IJ! /3/2)-1/3 0491 1972 IJ! /3 + 3v'5/4 0492 1818 2X : In 2/10 04923355 sr : /2/4 + 4/5 0492 3431 eu : In(ln 2) 0492 4623 J 1 : In(e/3) 0492 5509 rt : (9,1,-6,3) 0492 5801 Ei : 9/25 0492 5924 eu : e/3 - 37r / 4 0492 6062 rt : (8,2,-9,-2) 0492 7853 lOX : P42 04928002 er : 51n 2/3 04930614 In : (e/3)1/2 0493 0700 J2 : 2/5/7 0493 2594 sr : 1O~/3 04934417 (: (5/3)3 0493 4783 Ei : 2~/7 04935475 at : 1/4 + 2/5/3 0493 6777 rt : (9,2,-4,4) 0493 7336 rt : (8,1,-7,-3) 0493 8271 sq : 2/9 0493 8728 rt : (6,6,-9,8) 04938948 IJ!

2/4 - 3/3/4 0562 6823 J 2 : 13/19 0568 2553 2'" : 3 + 3e/2 05627289 II! /2/2 0563 2557 II! /2/4 - 3/3 0563495710'" : 7In2/10 05689874 11O : 2(/5/3 05635126 e'" : 5(e + 71")/6 05690262 rt : (3,7,-5,5) 0563 5297 rt : (4,1,3,-9) 0569 0769 rt : (1,7,0,-9) 0569 1237 12 : 3e/2 + 471" 0563 5917 S7l" : 1/4 + /3 05636265 rt : (3,5,1,7) 05691682 II!

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