The best kernel,as far as appx. after 20 terms, for Zeta(, 2, ) is 2 (z!) ----------------- 2 ((2 x + z + 1)!) the error is, -.322299966013187640000259698116180705508354944735919357090400378886182514 -27 10 -76 The error with 60 terms is, -.45824624052722793156139 10 The correponding MWZ pair is 2 3 3 (z!) (x + 1) (2 x + 1) 4 3 [-----------------, [[2 -------------------]], [1], [1/2 (120 x + 372 x 2 (1 + 4 x) (3 + 4 x) ((2 x + z + 1)!) 3 2 2 2 2 2 3 + 136 z x + 56 z x + 426 x + 316 z x + 242 x z + 86 z x + 8 z x 2 3 / + 213 x + 39 + 33 z + 6 z + 61 z) / ((1 + 4 x) (3 + 4 x) / 2 (2 x + z + 2) )]] The corresponding Acceleration scheme is 3 1 (x + 1) (2 x + 1) [--------, [[1/2 ------------------------------]], 2 2 (1 + z) (1 + 4 x) (3 + 4 x) (2 x + 3) 3 2 40 x + 84 x + 58 x + 13 [3/8 ---------------------------]] (x + 1) (1 + 4 x) (3 + 4 x) The best kernel,as far as appx. after 20 terms, for Zeta(, 3, ) is 2 (z!) ----------------------------- 2 ((2 x + z + 1)!) (x + z + 1) the error is, -.84893521865190552158722526204376023172963887988374551341519817336050638 -28 10 -77 The error with 60 terms is, -.7257157215884935214944 10 The correponding MWZ pair is 2 (z!) 4 3 2 [-----------------------------, [[(x + 1) ]], [1], [1/4 (30 x + 79 x + 68 x 2 ((2 x + z + 1)!) (x + z + 1) 2 2 2 3 / + 19 + 34 z x + 59 x z + 25 z + 14 z x + 12 z + 2 z ) / ((2 x + 1) / 2 (2 x + z + 2) )]] The corresponding Acceleration scheme is 3 1 (x + 1) 30 x + 19 [--------, [[1/4 ------------------]], [1/16 ---------]] 3 2 2 x + 1 (1 + z) (x + 2) (2 x + 3) The best kernel,as far as appx. after 20 terms, for Zeta(, 4, ) is z! --------------------------- 3 (2 x + z + 1)! (x + z + 1) the error is, -.3206357713469676129186860234747254900539835714131263499427958\ -14 615954807871200022777773 10 The error with 60 terms is, -39 -.561599524122443927302109987563564900555617003344636234282323 10 The correponding MWZ pair is z! [---------------------------, [ 3 (2 x + z + 1)! (x + z + 1) 2 3 [2 x + 3, -(x + 1) (x + 5 x + 5), (x + 3) (x + 1) ], 3 2 [2 x + 4, -(3 x + 5) (x + 1), 2 (x + 1) ], [1, -x - 1, 0]], [1, z, z ], [ 2 2 3 2 z + 4 z x + 6 x z + 20 x + 4 + 8 x + 16 x 3 2 1/2 ----------------------------------------------, 1/2 (z + 5 z + 7 z (2 x + 1) (x + 1) (2 x + z + 2) 3 2 3 2 2 2 3 + 14 z x + 28 x z + 35 z x + 2 z x + 15 z x + 10 z x + 7 x + 5 x 2 4 3 2 + 9 x + 2 x + 1)/((2 x + 1) (x + 1) (2 x + z + 2)), 1/2 (9 z + 13 z 2 3 4 4 3 3 2 + 5 z + 3 z x - 7 z x + 2 z + 11 x z - 4 z x + 17 z x + 8 z x 2 2 2 2 3 4 2 3 4 5 + 34 z x + 29 z x + 8 z x + 2 z x - 2 x - 8 x - 7 x - 2 x + 2 x + 1)/((2 x + 1) (x + 1) (2 x + z + 2))]] The corresponding Acceleration scheme is 2 2 2 1 x + 2 x + 1 (x + 1) (x + 5 x + 5) (x + 2 x + 1) [--------, [[1/2 ------------, - 1/2 -------------------------------------, 4 3 3 (1 + z) (x + 2) (x + 2) (2 x + 3) 3 2 2 (x + 3) (x + 1) (x + 2 x + 1) x + 2 x + 1 1/2 -------------------------------], [------------------, 3 2 (x + 2) (2 x + 3) (2 x + 3) (x + 2) 2 3 2 (3 x + 5) (x + 1) (x + 2 x + 1) (x + 1) (x + 2 x + 1) - 1/2 --------------------------------, -----------------------], 3 3 (x + 2) (2 x + 3) (x + 2) (2 x + 3) 2 2 x + 2 x + 1 (x + 1) (x + 2 x + 1) [1/2 ------------------, - 1/2 ----------------------, 0]], 3 3 (x + 2) (2 x + 3) (x + 2) (2 x + 3) 3 2 2 x + 3 x - 1 [1, 1/4 x + 1/4, - 1/4 ---------------]] 2 x + 1 The best kernel,as far as appx. after 20 terms, for Zeta(, 5, ) is z! --------------------------- 4 (2 x + z + 1)! (x + z + 1) the error is, -.1455967172298989793317132104782647309316320822921699032667998\ -15 16579393127044005821210 10 The error with 60 terms is, -41 -.9056888495615087931959666141023620146721268063333287568152 10 The correponding MWZ pair is z! [---------------------------, [[2 x + 3, 2 x + 3, 4 (2 x + z + 1)! (x + z + 1) 3 2 3 2 2 -(x + 1) (x + 7 x + 17 x + 13), (2 x + 13 x + 28 x + 19) (x + 1) ], [ 2 2 x + 4, 4 x + 7, -2 (x + 1) (2 x + 10 x + 11), 2 2 (7 x + 30 x + 29) (x + 1) ], 2 [1, 2 x + 5, -6 (x + 2) (x + 1), 2 (4 x + 7) (x + 1) ], 2 2 3 [0, 1, -2 - 2 x, 2 (x + 1) ]], [1, z, z , z ], [ 2 2 3 2 z + 4 z x + 6 x z + 20 x + 4 + 8 x + 16 x 1/2 ----------------------------------------------, (2 x + 1) (x + 1) (2 x + z + 2) 2 2 2 2 2 3 4 z + 6 z x + 4 z x + 2 z + 20 z x + 16 x z + 8 z x 2 1/2 ---------------------------------------------------------, 1/2 (14 x (x + 1) (2 x + 1) (2 x + z + 2) 4 5 2 4 3 4 3 2 + 6 x + 1 + 9 x + 2 x + 36 z x + 4 z + 2 z x + 6 z + z + 12 z x 3 2 2 2 2 3 2 4 3 + 18 z x + 50 z x + 40 z x + 20 z x + 10 z + 8 z x + 28 z x 3 + 20 x z + 16 x )/((x + 1) (2 x + 1) (2 x + z + 2)), 1/2 (2 z - 4 x 2 2 3 6 3 2 2 2 - 20 x - 6 x z + 8 z - 40 x - 4 x - 76 z x - 44 z x - 24 z x 2 3 4 3 5 4 2 3 3 2 + 8 z x + 36 z x - 40 x + 16 z - 20 x - 54 z x - 40 z x + 24 z x 4 4 5 4 2 5 5 3 3 2 4 + 18 z x + 10 z + 2 z + 8 z x - 14 z x + 2 z x + 4 z x - 16 z x )/((x + 1) (2 x + 1) (2 x + z + 2))]] The corresponding Acceleration scheme is 1 %1 %1 [--------, [[1/2 --------, 1/2 --------, 5 4 4 (1 + z) (x + 2) (x + 2) 3 2 (x + 1) (x + 7 x + 17 x + 13) %1 - 1/2 ----------------------------------, 4 (x + 2) (2 x + 3) 3 2 2 (2 x + 13 x + 28 x + 19) (x + 1) %1 %1 1/2 --------------------------------------], [------------------, 4 3 (x + 2) (2 x + 3) (2 x + 3) (x + 2) 2 (4 x + 7) %1 (x + 1) (2 x + 10 x + 11) %1 1/2 ------------------, - -----------------------------, 4 4 (x + 2) (2 x + 3) (x + 2) (2 x + 3) 2 2 (7 x + 30 x + 29) (x + 1) %1 %1 1/2 ------------------------------], [1/2 ------------------, 4 4 (x + 2) (2 x + 3) (x + 2) (2 x + 3) 2 (2 x + 5) %1 (x + 1) %1 (4 x + 7) (x + 1) %1 1/2 ------------------, -3 ------------------, ---------------------], 4 3 4 (x + 2) (2 x + 3) (x + 2) (2 x + 3) (x + 2) (2 x + 3) 2 %1 (x + 1) %1 (x + 1) %1 [0, 1/2 ------------------, - ------------------, ------------------]], 4 4 4 (x + 2) (2 x + 3) (x + 2) (2 x + 3) (x + 2) (2 x + 3) 2 %1 x [1, 0, 1/4 x + 1/2 x + 1/4, - -------]] 2 x + 1 3 2 %1 := x + 3 x + 3 x + 1 The best kernel,as far as appx. after 20 terms, for Zeta(, 6, ) is 6 (z!) ----------------- 6 ((2 x + z + 1)!) the error is, -.6983083882995772798580073062814191882433684835355769758476274\ -6 26322561717172734288481650587230 10 The error with 60 terms is, -.16764190647618415125566261063096859531040106395\ -7 817466095220776994776508565671544506053769852 10 The correponding MWZ pair is 6 (z!) 2 3 [-----------------, [[2/3 (1778469 + 17989716 x + 80565168 x + 210056486 x 6 ((2 x + z + 1)!) 4 5 6 7 8 + 352643652 x + 397893072 x + 305390048 x + 157437056 x + 52209408 x 9 10 3 3 + 10069120 x + 858880 x ) (x + 1) (2 x + 1) /((12 x + 11) (3 + 4 x) 13 12 (12 x + 7) (12 x + 5)), - 14/9 (81050112 x + 1026634752 x 11 10 9 8 + 5893903488 x + 20302073984 x + 46816388032 x + 76341637120 x 7 6 5 4 + 90604565832 x + 79280434016 x + 51168416846 x + 24066320830 x 3 2 3 + 8019126462 x + 1792482927 x + 240803817 x + 14670810) (2 x + 1) 4 (x + 1) /((12 x + 11) (6 x + 5) (3 x + 2) (3 + 4 x) (12 x + 7) (12 x + 5) 16 15 14 (1 + 3 x)), 14/9 (324200448 x + 4863006720 x + 33768804864 x 13 12 11 + 144044378112 x + 422258261248 x + 901493198336 x 10 9 8 + 1448947534624 x + 1787078472096 x + 1707915333048 x 7 6 5 4 + 1267912322496 x + 728068633728 x + 319667440360 x + 105089124296 x 3 2 3 + 24974008948 x + 4039823589 x + 396655617 x + 17766210) (x + 1) 3 (2 x + 1) /((12 x + 11) (6 x + 5) (3 x + 2) (3 + 4 x) (12 x + 7) (12 x + 5) 16 15 (1 + 3 x) (1 + 4 x)), 14/9 (1971800064 x + 24341031936 x 14 13 12 + 134346312192 x + 435173844224 x + 908277733376 x 11 10 9 + 1245584123008 x + 1045608943264 x + 310653181488 x 8 7 6 5 - 450227769480 x - 756235083092 x - 606504038684 x - 314345230456 x 4 3 2 - 111204313870 x - 26690272902 x - 4146287877 x - 373978641 x 4 4 - 14753970) (x + 1) (2 x + 1) /((12 x + 11) (6 x + 5) (3 x + 2) (3 + 4 x) (12 x + 7) (12 x + 5) (1 + 3 x) (1 + 4 x) (6 x + 1)), - 14/9 ( 20 19 18 188654469120 x + 2944234635264 x + 21344202584064 x 17 16 15 + 95456449622016 x + 294963699581952 x + 668357326155776 x 14 13 12 + 1150121869831680 x + 1535659257516800 x + 1611339587282624 x 11 10 9 + 1337065694210880 x + 878133691188848 x + 454414463209088 x 8 7 6 + 183306060531012 x + 56546370446104 x + 12905352223692 x 5 4 3 2 + 2048487862242 x + 195136151782 x + 4974313756 x - 1117162809 x 3 3 - 125297301 x - 4086090) (x + 1) (2 x + 1) /((1 + 4 x) (12 x + 1) (6 x + 1) (12 x + 5) (1 + 3 x) (12 x + 7) (6 x + 5) (3 x + 2) (3 + 4 x) 8 7 6 (12 x + 11))], [56/3 (x + 2) (108160 x + 873184 x + 3018976 x 5 4 3 2 + 5825184 x + 6869520 x + 5082102 x + 2309220 x + 590622 x + 65241) 3 3 (x + 1) (2 x + 1) /((12 x + 11) (3 + 4 x) (12 x + 7) (12 x + 5)), - 8/3 ( 12 11 10 9 130242816 x + 1443039552 x + 7178052384 x + 21209887232 x 8 7 6 5 + 41503969824 x + 56722018476 x + 55568517822 x + 39349035654 x 4 3 2 + 19999317764 x + 7116762151 x + 1682859693 x + 237288028 x + 15070440) 3 4 (2 x + 1) (x + 1) /((12 x + 11) (6 x + 5) (3 x + 2) (3 + 4 x) (12 x + 7) 15 14 (12 x + 5) (1 + 3 x)), 8/9 (1134701568 x + 15413029632 x 13 12 11 + 96696832128 x + 371380716416 x + 975346600704 x 10 9 8 + 1852583474640 x + 2624943268536 x + 2821115160144 x 7 6 5 4 + 2315663458608 x + 1450025979376 x + 686242629252 x + 240772900650 x 3 2 3 + 60543731175 x + 10284173967 x + 1053101484 x + 48884220) (x + 1) 3 (2 x + 1) /((12 x + 11) (6 x + 5) (3 x + 2) (3 + 4 x) (12 x + 7) (12 x + 5) 15 14 (1 + 3 x) (1 + 4 x)), 8/3 (4018000896 x + 44890949376 x 13 12 11 + 224170114560 x + 659603947456 x + 1266934439168 x 10 9 8 7 + 1655500452272 x + 1471814158624 x + 835874931324 x + 217073380700 x 6 5 4 3 - 79426122708 x - 107906660362 x - 53271114520 x - 15365564649 x 2 4 4 - 2687167865 x - 263011252 x - 10995600) (x + 1) (2 x + 1) /((12 x + 11) (6 x + 5) (3 x + 2) (3 + 4 x) (12 x + 7) (12 x + 5) (1 + 3 x) (1 + 4 x) 19 18 (6 x + 1)), - 8/9 (907620360192 x + 12893857966080 x 17 16 15 + 84815563004928 x + 343030030027776 x + 955175198249984 x 14 13 12 + 1942895300099328 x + 2988955579499520 x + 3552115194238784 x 11 10 9 + 3301939095594336 x + 2415649340151720 x + 1392146506202548 x 8 7 6 + 629525911697184 x + 221358325636008 x + 59624284858846 x 5 4 3 2 + 12027477100302 x + 1757486431266 x + 177001862685 x + 11359885461 x 3 3 + 404148372 x + 5751180) (x + 1) (2 x + 1) /((1 + 4 x) (12 x + 1) (6 x + 1) (12 x + 5) (1 + 3 x) (12 x + 7) (6 x + 5) (3 x + 2) (3 + 4 x) 8 7 6 5 (12 x + 11))], [28 (98592 x + 822640 x + 2909880 x + 5706012 x 4 3 2 3 + 6808696 x + 5082066 x + 2325246 x + 598034 x + 66363) (x + 1) 3 (2 x + 1) /((12 x + 11) (3 + 4 x) (12 x + 7) (12 x + 5)), - 28/3 ( 11 10 9 8 38975040 x + 367660800 x + 1542657984 x + 3810824896 x 7 6 5 4 + 6170531956 x + 6886322976 x + 5409982958 x + 2993440184 x 3 2 3 4 + 1143348294 x + 286996029 x + 42571293 x + 2822490) (2 x + 1) (x + 1) /((12 x + 11) (6 x + 5) (3 x + 2) (3 + 4 x) (12 x + 7) (12 x + 5) (1 + 3 x) 14 13 12 11 ), 4/3 (376434432 x + 4797441792 x + 28370857728 x + 102358717568 x 10 9 8 7 + 249754062256 x + 433705033584 x + 551178588936 x + 520081201936 x 6 5 4 3 + 365948059704 x + 191037075688 x + 72811217206 x + 19635768336 x 2 3 3 + 3538347813 x + 380751211 x + 18417630) (x + 1) (2 x + 1) /((12 x + 11) (6 x + 5) (3 x + 2) (3 + 4 x) (12 x + 7) (12 x + 5) (1 + 3 x) (1 + 4 x)), 14 13 12 4/3 (10896028416 x + 107372184192 x + 471629741568 x 11 10 9 + 1221056273536 x + 2073374829936 x + 2425722725896 x 8 7 6 5 + 1992125558776 x + 1140475731916 x + 435450270160 x + 95468625336 x 4 3 2 + 3160809316 x - 4676046822 x - 1380169317 x - 170634099 x - 8142750) 4 4 (x + 1) (2 x + 1) /((12 x + 11) (6 x + 5) (3 x + 2) (3 + 4 x) (12 x + 7) 18 (12 x + 5) (1 + 3 x) (1 + 4 x) (6 x + 1)), - 4/3 (632499259392 x 17 16 15 + 8109875644416 x + 48024119937024 x + 174327595826688 x 14 13 12 + 434090590371584 x + 786239959448832 x + 1071870977535168 x 11 10 9 + 1122830358435872 x + 914648538458920 x + 582594523865496 x 8 7 6 + 290227334949892 x + 112531368466572 x + 33616355763420 x 5 4 3 2 + 7609589560018 x + 1272703346916 x + 151297671408 x + 12001474839 x 3 3 + 564476473 x + 11747370) (x + 1) (2 x + 1) /((1 + 4 x) (12 x + 1) (6 x + 1) (12 x + 5) (1 + 3 x) (12 x + 7) (6 x + 5) (3 x + 2) (3 + 4 x) 3 3 (x + 2) %1 (x + 1) (2 x + 1) (12 x + 11))], [56/3 -------------------------------------------, - 56/9 ( (12 x + 11) (3 + 4 x) (12 x + 7) (12 x + 5) 10 9 8 7 6 26698464 x + 206193312 x + 708073680 x + 1425065120 x + 1862407582 x 5 4 3 2 + 1651736326 x + 1006588970 x + 415993815 x + 111470739 x + 17462772 x 3 4 + 1211760) (2 x + 1) (x + 1) /((12 x + 11) (6 x + 5) (3 x + 2) (3 + 4 x) 13 12 (12 x + 7) (12 x + 5) (1 + 3 x)), - 56/9 (31224960 x + 225718272 x 11 10 9 8 + 534997824 x - 4473600 x - 2774066232 x - 7178404304 x 7 6 5 4 - 10096881568 x - 9270644760 x - 5862819236 x - 2582150788 x 3 2 3 3 - 778947201 x - 153327795 x - 17697012 x - 904860) (x + 1) (2 x + 1) /( (12 x + 11) (6 x + 5) (3 x + 2) (3 + 4 x) (12 x + 7) (12 x + 5) (1 + 3 x) 13 12 11 (1 + 4 x)), 8/9 (10320580224 x + 86617217088 x + 323916369024 x 10 9 8 7 + 714837041696 x + 1037170112936 x + 1041553734964 x + 741060196332 x 6 5 4 3 + 375362579168 x + 133797341986 x + 32541503698 x + 5080754469 x 2 4 4 + 449384511 x + 15901404 x - 138600) (x + 1) (2 x + 1) /((12 x + 11) (6 x + 5) (3 x + 2) (3 + 4 x) (12 x + 7) (12 x + 5) (1 + 3 x) (1 + 4 x) 17 16 (6 x + 1)), - 8/9 (433106279424 x + 5001845022720 x 15 14 13 + 26638093444608 x + 86552593143552 x + 191756653156992 x 12 11 10 + 307009342526464 x + 367453610808864 x + 335500475710544 x 9 8 7 + 236321352101036 x + 128987115161112 x + 54469767466468 x 6 5 4 3 + 17663241408766 x + 4335339452466 x + 786532413824 x + 101536451085 x 2 3 3 + 8749239063 x + 446013732 x + 9997380) (x + 1) (2 x + 1) /((1 + 4 x) (12 x + 1) (6 x + 1) (12 x + 5) (1 + 3 x) (12 x + 7) (6 x + 5) (3 x + 2) 3 3 %1 (x + 1) (2 x + 1) (3 + 4 x) (12 x + 11))], [14/3 -------------------------------------------, (12 x + 11) (3 + 4 x) (12 x + 7) (12 x + 5) 3 4 %1 (2 x + 1) (x + 1) 9 - 14/3 -------------------------------------------, - 14/9 (2282176 x (12 x + 11) (3 + 4 x) (12 x + 7) (12 x + 5) 8 7 6 5 4 + 11051040 x + 22275888 x + 23467768 x + 12577896 x + 1548408 x 3 2 3 3 - 2044368 x - 1238328 x - 286842 x - 24453) (x + 1) (2 x + 1) /( 8 (12 x + 11) (3 + 4 x) (12 x + 7) (12 x + 5) (1 + 4 x)), 14 (505440 x 7 6 5 4 3 + 2433392 x + 5005384 x + 5714356 x + 3931840 x + 1653872 x 2 4 4 + 410498 x + 54440 x + 3003) (x + 1) (2 x + 1) /((12 x + 11) (3 + 4 x) 12 11 (12 x + 7) (12 x + 5) (1 + 4 x)), - 2/9 (763176704 x + 7126477824 x 10 9 8 7 + 27793053120 x + 61560735616 x + 87371551920 x + 84215381328 x 6 5 4 3 + 56652775196 x + 26790774012 x + 8816831040 x + 1959647070 x 2 3 3 + 276785100 x + 21914580 x + 702225) (x + 1) (2 x + 1) /((1 + 4 x) (12 x + 1) (12 x + 5) (12 x + 7) (3 + 4 x) (12 x + 11))]], 2 3 4 10 [1, z, z , z , z ], [1/36 (82619460 z + 1061278722 x + 151366762912512 x 2 2 3 + 18275592384 x + 3226020282 x z + 107151660 z + 182547805734 x 6 3 2 + 18618667911732 x + 515109409668 z x + 53726080806 z x 2 2 2 3 + 65157457644 z x + 4064256162 z x + 2811628242 z x 9 4 3 5 + 133897887114432 x + 1197712605096 x + 76521060 z + 5520956551488 x 7 8 4 7 + 83160 z + 11870443080000 x z + 47102593295184 x 11 12 8 + 129969123922176 x + 83249901568512 x + 90717187393056 x 6 4 2 3 3 2 + 1288980 z + 3218994877716 z x + 595930893498 z x + 43203118554 z x 4 4 5 14 + 1174316670 z x + 33056100 z + 8690220 z + 12156380716032 x 13 15 16 + 38516941145088 x + 2341401624576 x + 207597551616 x 10 2 5 5 6 4 + 140957051399424 x z + 471983975712 z x + 17501513400 z x 7 2 6 2 6 + 33226380 z x + 565315038 z x + 44242727811024 z x 5 2 6 7 7 5 + 4164799482 z x + 42619266 z x + 2647692 x z + 2077638336 z x 6 6 7 3 3 5 + 88158798144 x z + 39821478996480 x z + 7810322242968 z x 4 4 4 3 5 3 + 724914549900 z x + 140908826970 z x + 31934274948 z 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1) (12 x + 5) (12 x + 7) / 6 (3 + 4 x) (3 x + 2) (6 x + 5) (12 x + 11) (2 x + z + 2) )]] %1 := 6 5 4 3 2 93808 x + 422136 x + 791556 x + 791658 x + 445428 x + 133704 x + 16731 The corresponding Acceleration scheme is 1 2 3 [--------, [[1/96 (1778469 + 17989716 x + 80565168 x + 210056486 x 6 (1 + z) 4 5 6 7 8 + 352643652 x + 397893072 x + 305390048 x + 157437056 x + 52209408 x 9 10 3 / 3 + 10069120 x + 858880 x ) (2 x + 1) / ((x + 1) (12 x + 11) (3 + 4 x) / 6 13 12 (12 x + 7) (12 x + 5) (2 x + 3) ), - 7/288 (81050112 x + 1026634752 x 11 10 9 8 + 5893903488 x + 20302073984 x + 46816388032 x + 76341637120 x 7 6 5 4 + 90604565832 x + 79280434016 x + 51168416846 x + 24066320830 x 3 2 3 / + 8019126462 x + 1792482927 x + 240803817 x + 14670810) (2 x + 1) / ( / 2 (x + 1) (12 x + 11) (6 x + 5) (3 x + 2) (3 + 4 x) (12 x + 7) (12 x + 5) 6 16 15 (1 + 3 x) (2 x + 3) ), 7/288 (324200448 x + 4863006720 x 14 13 12 11 + 33768804864 x + 144044378112 x + 422258261248 x + 901493198336 x 10 9 8 + 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(2 x + 3) )], [ 3 %1 (2 x + 1) 7/96 ---------------------------------------------------------------, 3 6 (x + 1) (12 x + 11) (3 + 4 x) (12 x + 7) (12 x + 5) (2 x + 3) 3 %1 (2 x + 1) - 7/96 ---------------------------------------------------------------, - 2 6 (x + 1) (12 x + 11) (3 + 4 x) (12 x + 7) (12 x + 5) (2 x + 3) 9 8 7 6 5 7/288 (2282176 x + 11051040 x + 22275888 x + 23467768 x + 12577896 x 4 3 2 3 / + 1548408 x - 2044368 x - 1238328 x - 286842 x - 24453) (2 x + 1) / / 3 6 ((x + 1) (12 x + 11) (3 + 4 x) (12 x + 7) (12 x + 5) (1 + 4 x) (2 x + 3) ) 8 7 6 5 4 , 7/32 (505440 x + 2433392 x + 5005384 x + 5714356 x + 3931840 x 3 2 4 / 2 + 1653872 x + 410498 x + 54440 x + 3003) (2 x + 1) / ((x + 1) / 6 (12 x + 11) (3 + 4 x) (12 x + 7) (12 x + 5) (1 + 4 x) (2 x + 3) ), - 1/288 12 11 10 9 (763176704 x + 7126477824 x + 27793053120 x + 61560735616 x 8 7 6 5 + 87371551920 x + 84215381328 x + 56652775196 x + 26790774012 x 4 3 2 + 8816831040 x + 1959647070 x + 276785100 x + 21914580 x + 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