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The Mathematically Inclined: Identity needed

Here's my work so far:
4^s * Zeta(s) = Zeta(s, 1/4) + Zeta(s, 1/2) + Zeta(s, 3/4) + Zeta(s)

Zeta(s,...1/2) = (2^s-1) * Zeta(s)

4^s * Zeta(s) - Zeta(s) - (2^s-1) * Zeta(s) = Zeta(s, 1/4) + Zeta(s, 3/4)...... looking for a way to either extract the two or find some kind of ratio that'll transform the Zeta(s,...1/4) + Zeta(s, 3/4) into a Zeta(s, 1/4) - Zeta(s, 3/4) using only the left-hand arguments.

Joey_21 - June 07, 2003, 04:02:02 - https://www.hard-light.net/forums/index.php?topic=15567.msg297769#msg297769
Iraq - The Great Thread - all war news goes here

Originally posted by Razor




If dysfunction is a function, then I must be some kind of GENIUS-S-S-S-S-S-S-S

01010 - March 27, 2003, 03:00:53 - https://www.hard-light.net/forums/index.php?topic=13858.msg266070#msg266070
is it jut me or are there "s"es popping up everywhere

s whast's s the s problem s?

Knight Templar - April 01, 2003, 10:58:04 - https://www.hard-light.net/forums/index.php?topic=14232.msg268541#msg268541
Which is better?

[chant]P S 2, P S 2, P S 2, P S 2, P S 2[/chant]

Dr.Zer0 - June 19, 2002, 06:09:02 - https://www.hard-light.net/forums/index.php?topic=8245.msg145563#msg145563
Profile shot of the Xanthus Class Carrier

C u r s e s ! * s h a k e s h a n d *

Shrike - May 04, 2001, 04:56:00 - https://www.hard-light.net/forums/index.php?topic=2961.msg40787#msg40787
Re: Redefining the word '****'

*Is s-s-s-soooo skeered*

Except not.

Unknown Target - January 23, 2007, 06:48:11 - https://www.hard-light.net/forums/index.php?topic=44906.msg916068#msg916068
Which is better?

Quote Originally posted by Dr.Zer0
[chant]P S 2, P S 2, P S 2, P S 2, P S 2[/chant]

Amen

delta_7890 - June 19, 2002, 11:16:13 - https://www.hard-light.net/forums/index.php?topic=8245.msg145720#msg145720
Re: BP: War in Heaven discussion

The way I beat "Her Finest Hour":
Spoiler: 1, F8, 2, F7, C-3-5, F8, 2, F9, S, S, S, S, S, S, S, C-3...-4, F9, S, S, S, S, S, S, S, C-3-4, F8, 2, F9, F9, F9, C-1-1-1, F9, C-1-2-1, F9, C-1-3-1, F8, 2, F6,

LordPomposity - January 08, 2013, 05:00:19 - https://www.hard-light.net/forums/index.php?topic=70746.msg1664579#msg1664579
Sorry, Europe

no sweeds arnt suppsoed to do that they are simply supposed to pronounce "j"s as "y"s and "ch"s as "sh"s

Splinter - May 02, 2004, 06:41:07 - https://www.hard-light.net/forums/index.php?topic=23329.msg463651#msg463651
The Mathematically Inclined: Identity needed

zeta functions, so there would probably not be any recurrence relation for it (a recurrence formula in s...for z (s,x) would be completely revolutionary and solve almost all the zeta function problems )....I accidentally typed 'x' instead of 's'....Here's what I've gathered so far:

[Zeta(s, 1/4) + Zeta(s, 3/4)] / 2^s = Zeta(s, 1/2)

Zeta(s, 1/2) /...(2^s - 1) = Zeta(s)

Zeta(s) * (2^s - 1) * 2^s = Zeta(s, 1/4) + Zeta(s, 3/4)

And after all of that,

Joey_21 - June 07, 2003, 05:27:03 - https://www.hard-light.net/forums/index.php?topic=15567.msg297791#msg297791
Exciting new breakthrough in mathematics!

The Justin Moore-Minutes Theory of General Sleepiness

s (a) = Sleepiness, actual
s (p) = Sleepiness...obligations
l = lightness of sky outside window

--------------------------------------------

s...(a) ≠ s (p)
s (a) ∝ t -1
s (p) ∝ p
s (p) ∝ l -1
s (p) = [( t × w ) ÷ l...] ÷ p

solve for s (p)


erm, off to bed

Rictor - November 13, 2005, 10:54:47 - https://www.hard-light.net/forums/index.php?topic=36806.msg752600#msg752600
"A new kind of fighter, uh?"

It´s a bird!!
It´s a plane!!
No, it´s just a cube...

Swamp_Thing - August 09, 2004, 01:49:34 - https://www.hard-light.net/forums/index.php?topic=26061.msg522807#msg522807
The Big Eyecandy Thread (warning: lots of images)

PBanks: ( "S-B-AAA" )
$Subsystem: turret03,1,1.0
 $Default SBanks: ( "S-AF-Cluster-B" )
$Subsystem:..."S-B-Small" )
$Subsystem: turret06,1,1.0
 $Default PBanks: ( "S-B-Small" )
$Subsystem: turret07,3,1.0... $Default PBanks: ( "S-B-Small" )
$Subsystem: turret08,4,1.0
 $Default PBanks: ( "S-AF-Las-A" )
$Subsystem...: turret09,4,1.0
 $Default PBanks: ( "S-AF-Las-A" )
$Subsystem: turret10,1,1.0
 $Default PBanks: ( "S-AF-Las-A... $Default PBanks: ( "S-AF-Flak-B" )
$Subsystem: turret15,1,1.0
 $Default PBanks: ( "S-AF-Flak-B" )
$

Woomeister - December 31, 2004, 04:18:26 - https://www.hard-light.net/forums/index.php?topic=23486.msg593338#msg593338
Re: Animation Code woes

s = s0 + v0t + att/2 || s0 = S(1), v0 = 0, t = V(maximum) / a
S(2) = S(1) + V(maximum)V(maximum)/2a...= vt || v = V(maximum), s = S(turnpoint) - S(2)
S(turnpoint) - S(initial) + V(initial)V(initial)/2a...s = m/s / m/s^2 + m/s / m/s^2 + (m - m + ((m/s)^2 - (m/s)^2)/m/s^2) / m/s
= s + s + (m + (m^...2/s^2)/ m/s^2) m/s
= s + ( m )/ m/s
= s
 -----------------------------------------------...= s0 + v0 t + att/2 || s0 = 0, v0 = 0, s = (S(final) - S(1)) / 2
(S(final) - S(1)) / 2 = a/2 * T(intercept

Wanderer - February 03, 2010, 03:05:39 - https://www.hard-light.net/forums/index.php?topic=67912.msg1341110#msg1341110
Re: Balancing the EU and US in an RTS game

america wins every single match

U S A     U S A     U S A

Hades - August 19, 2015, 07:17:45 - https://www.hard-light.net/forums/index.php?topic=90304.msg1793623#msg1793623
Re: Capital ships - the use in FS1?

Maybe it`s the GTVA`s solution to overpopulation...

Or maybe that`s where they put their prisoners.

Fenrir - June 28, 2008, 03:22:33 - https://www.hard-light.net/forums/index.php?topic=54518.msg1109453#msg1109453
Re: Terran, Vasudan and Shivan Technology

Flak (1400 m,  0.15 s,  700 mps,  200 HP/s, total 1200 HP/s- although it'll max out only against big...ships due to spread),
2 AAAf's (1500 m,  5.5 s,   24 HP/s, total 48 HP/s)
2 SGreens (4000 m,  45 s, ...61 HP/s, total 122 HP/s)...., total 250 HP/s),
Shivan Cluster x 2  (450 m,  20 s,  90 mps,  3 HP/s missile+ 12 HP/s for the 8 bomblets...each missile launches, total 30 HP/s)
Anti-Fighter Beam x 1 (1500 m,  5 s, 20 HP/s, total 40 HP/s),

BengalTiger - December 20, 2007, 11:44:52 - https://www.hard-light.net/forums/index.php?topic=50848.msg1031622#msg1031622
The Mathematically Inclined: Identity needed

Hmm... another identity I noticed:

-2 + [Zeta(s, 1/4) + Zeta(s, 3/4)] / Zeta(s, 3/4) = [Zeta(s, 1/4)...- Zeta(s, 3/4)] / Zeta(s, 3/4)

Although it doesn't help me out just yet, this may help with finding

Joey_21 - June 07, 2003, 10:45:19 - https://www.hard-light.net/forums/index.php?topic=15567.msg297837#msg297837
Re: A celebration of Freespace

I suggest removing the (s) from action(s) and condition(s) in the tech entry.

Scotty - December 09, 2009, 01:33:21 - https://www.hard-light.net/forums/index.php?topic=25406.msg1322599#msg1322599
Re: FreeSpace Open Installer! Download it now!

With the installer, it only downloaded 3.6.9's no 3.6.10's. Should it have downloaded any 3.6.10's?

HTWingNut - May 04, 2008, 06:16:19 - https://www.hard-light.net/forums/index.php?topic=42854.msg1084629#msg1084629