Catalan's Constant [ramanujan's Formula]
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Catalan's Constant [ramanujan's Formula]
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Infinity) also knownunder the name beta(2), see ?catalan in Maple for more details.
The previous record was 200000 digits, also from Thomas Papanikolaouand before that: 100000 digitswas due to Greg Fee and Simon Plouffe on August 14, 1996, by using a SGI r10000 Power Challenge with 194 Mhz in 5. 63 hoursand the standard implementation of Catalan on MapleV, Release 4. (which uses Greg's idea).
Euler Tranform: References, Abramowitz and Stegun, formula 3. 6. 27page 16 in Handbook of Mathematical ...Functions and Tables, Dover 1964.
Ramanujan Notebooks, part I formula 34. 1 of page 293.
The series used is by putting x--> -1/2 . In otherwords the formula used is: the ordinary formula for Catalan sum((-1)**(n+1)/(2*n+1)**2, n=0. . Infinity) and then you apply the Euler Transform to it.
Computation of Catalan's constant using Ramanujan's Formula, byGreg Fee, ACM 1990, Proceedings of the ISAAC conference, 1990, p. 157.
What to read after Catalan's Constant [ramanujan's Formula]?
You can find similar books in the "Read Also" column, or choose other free books by Fee Greg to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
Infinity) also knownunder the name beta(2), see ?catalan in Maple for more details.
The previous record was 200000 digits, also from Thomas Papanikolaouand before that: 100000 digitswas due to Greg Fee and Simon Plouffe on August 14, 1996, by using a SGI r10000 Power Challenge with 194 Mhz in 5. 63 hoursand the standard implementation of Catalan on MapleV, Release 4. (which uses Greg's idea).
Euler Tranform: References, Abramowitz and Stegun, formula 3. 6. 27page 16 in Handbook of Mathematical ...Functions and Tables, Dover 1964.
Ramanujan Notebooks, part I formula 34. 1 of page 293.
The series used is by putting x--> -1/2 . In otherwords the formula used is: the ordinary formula for Catalan sum((-1)**(n+1)/(2*n+1)**2, n=0. . Infinity) and then you apply the Euler Transform to it.
Computation of Catalan's constant using Ramanujan's Formula, byGreg Fee, ACM 1990, Proceedings of the ISAAC conference, 1990, p. 157.
What to read after Catalan's Constant [ramanujan's Formula]?
You can find similar books in the "Read Also" column, or choose other free books by Fee Greg to read onlineMoreLess
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