<p> Γ(x) [15 D] Alvaro Same otherwise </p>

78cb9ebb-5c50-448f-a02e-bb7b4d27e193 2 4 5 decimal

&[DATE] &[TIME] - &[FILENAME]

Γ 0.99999999999999709182 57.156235665862923517 59.597960355475491248 - 14.136097974741747174 0.49191381609762019978 - 0.33994649984811888699 104 -^* 0.46523628927048575665 104 -^* 0.98374475304879564677 104 -^* - 0.15808870322491248884 103 -^* 0.21026444172410488319 103 -^* - 0.21743961811521264320 103 -^* 0.16431810653676389022 103 -^* - 0.84418223983852743293 104 -^* 0.26190838401581408670 104 -^* - 0.36899182659531622704 105 -^* 151 mat :

ζ Γ z ζ 1 - : zh z 0.5 + : zg zh 607128 / + : zp zg 0.5 zh *^: 14 mat 2 π * sqrt Γ 1 el Γ κ 1 + el z κ + / κ 114 sum + (* zp 2^* zg - exp * eval 21 line :

Valid for Re(ζ)>0

Source: Hart et al. "Computer Approximation" Copyright © 1968 by John Wiley & Sons,Inc. All rights reserved. No reproduction in any form of this book in whole or in part (except for brief quotation in critical articles or reviews), may be made whitout written authorization from the publisher.

JZERO 5852

|ε| = 23.22 decimals, [x] 0..8

p 1641556014884554375346147.435 394355966476729663601261.6471 - 21720183859245393139822.87997 481485995206981764828.5245941 - 5345457598841972345.381674607 33015389256896376.8646542622 - 118739068121104.2949874031474 247985116789.614443968987514 - 280314894.0831953934479400118 133662.5500481224741885945416 - 101 mat :

q 1641556014884554385346137.617 16033037244408932735390.45602 79130437776464052403.23616203 2613165313325.153278086066185 642960791882601.77592892131 1237672982083.40790348317773 1893012093.677918995179541438 2263381.356781110003609399116 1974.019272727281783930443513 1101 mat :

JONE 6054

|ε| = 25.02 decimals, [x] 0..8

a 1921176307760798128049021.316 222609203138739625477137.5773 - 7894463902082476734673.226741 126942437345360606543.6561036 - 1092152214043184787.101134641 5454629264396819.144157448868 - 16346594875712.84628830445048 29096627853.81647825756152444 - 28534334.51054763915026471449 11977.05712815379389149134705 - 101 mat :

b 3842352615521596256098041.912 35075670662720281057988.68716 161133431163341434400.7062889 492961231395985031.9632645381 1117536965288162.684489793105 1969278625584.719037168592923 2735606122.949877990248154504 2940957.355049651347475558106 2274.736606126590905134610965 1101 mat :

x J0 u x 2^11 line : p m el u m^* (m 110 sum q n el u n^* (n 110 sum / 21 line :

x J1 u x 2^11 line : x a m el u m^* (m 110 sum b n el u n^* (n 110 sum / * 21 line :

1.234567890123456789 J1 0.506915154862825

MCD 0.506915154862789 ≡

JONE can be safely extended to ~ twice its prescribed accuracy compared wrt Matlab "mwbesselj". This last one to be confirmed ?

|ε|= 23.22 decimals , [x] 0..8

x J0 x J1 2 1 sys

r x J1 x 1 - 18 solve :

rmw 1 x mwbesselj x 018 solve :

r 0 3.832 7.016 10.173 13.324 16.469 61 mat

rmw 0 3.832 7.016 10.173 13.324 16.471 61 mat

n x J 1 - (k^k! (k n + 1 + Γ * / x 2 / (n 2 k * +^* (k 011 sum :

x Γ

0 x J 1 x J 2 1 sys