The On-Line Encyclopedia of Integer Sequences® (OEIS®)

Revision History for A359282

(Underlined text is an addition; strikethrough text is a ~~deletion~~.)
Showing entries 1-10 | older changes

A359282

Decimal expansion of Integral_{x = 0..1} 1/x^(x^2) dx.
(history; published version)

#12 by Joerg Arndt at Wed Dec 28 02:03:28 EST 2022

STATUS

reviewed

approved

#11 by Michel Marcus at Wed Dec 28 00:22:03 EST 2022

STATUS

proposed

reviewed

#10 by Jon E. Schoenfield at Tue Dec 27 23:36:36 EST 2022

STATUS

editing

proposed

#9 by Jon E. Schoenfield at Tue Dec 27 23:36:34 EST 2022

NAME

Decimal expansion of Integral_{x = 0..1} 1/x^(x^2) dx.

STATUS

approved

editing

#8 by Peter Luschny at Tue Dec 27 14:52:43 EST 2022

STATUS

reviewed

approved

#7 by Joerg Arndt at Tue Dec 27 11:00:27 EST 2022

STATUS

proposed

reviewed

#6 by Peter Bala at Tue Dec 27 10:47:05 EST 2022

STATUS

editing

proposed

#5 by Peter Bala at Mon Dec 26 10:20:12 EST 2022

FORMULA

More generally, Integral_{x = 0..1} 1/x^(t*x^2) dx = Sum_{n >= 1} t^(n-1)/(2*n - 1)^n. See A253299 (case t = -1).

#4 by Peter Bala at Sat Dec 24 05:43:28 EST 2022

LINKS

Wikipedia, <a href="https://en.wikipedia.org/wiki/Sophomore%27s_dream">Sophomore's Dream</a>

#3 by Peter Bala at Sat Dec 24 05:05:04 EST 2022

	NAME	`allocatedDecimal forexpansion Peterof BalaIntegral_{x = 0..1} 1/x^(x^2) dx`
	DATA	`1, 1, 1, 9, 5, 4, 5, 1, 2, 0, 1, 3, 6, 1, 2, 7, 5, 9, 6, 6, 1, 2, 6, 7, 6, 2, 4, 7, 0, 2, 9, 8, 2, 7, 0, 3, 6, 4, 6, 0, 0, 4, 6, 9, 5, 7, 8, 7, 6, 4, 2, 7, 6, 2, 8, 9, 8, 6, 7, 4, 9, 5, 4, 6, 7, 5, 7, 0, 9, 4, 4, 0, 8, 3, 4, 4, 3, 2, 8, 3, 9, 8, 7, 5, 6, 8, 6, 2, 6, 4, 5, 3, 8, 2, 0, 1, 0, 7, 7, 3, 0, 0, 5, 9, 7, 9, 9, 4`
	OFFSET	`1,4`
	FORMULA	`Equals Sum_{n >= 1} 1/(2*n - 1)^n.`
	EXAMPLE	`1.119545120136127596612676247029827036460046957876427628986749 ...`
	MAPLE	`evalf(Sum(1/(2*n-1)^n, n = 1..infinity), 120);`
	MATHEMATICA	`NIntegrate[x^(-x^2), {x, 0, 1}, WorkingPrecision -> 103] // RealDigits // First`
	PROG	`(PARI) intnum(x = 0, 1, x^(-x^2))`
	CROSSREFS	`Cf. A073009, A083648, A253299, A359283, A359284, A359285, A359286.`
	KEYWORD	`allocated` `nonn,cons,easy`
	AUTHOR	`Peter Bala, Dec 24 2022`
	STATUS	`approved` `editing`

Last modified August 17 21:11 EDT 2024. Contains 375227 sequences. (Running on oeis4.)