任意の arctan(1/n) を 二項に展開する事を考える。
arctan(1/n) = arctan(1/p) + arctan(1/q)
両辺に tan を施すと、tanの加法定理より次式を得る。
n = (pq-1) / (p+q)
ここで p = n±m とおくと q = (n＾2±mn+1)/±m よって、
arctan(1/n) = arctan( 1/(n±m) ) + arctan( ±m/(n＾2±mn+1) )
以降、この展開式は加法定理にちなんで、加法展開と称することとする。
ｎ≦100 での展開可能な組み合わせは、下記のとおり。
| arctan(1/1) | arctan(1/2)+arctan(1/3) |
| arctan(1/2) | arctan(1/3)+arctan(1/7) |
| arctan(1/3) | arctan(1/2)-arctan(1/7)
arctan(1/4)+arctan(1/13) arctan(1/5)+arctan(1/8) |
| arctan(1/4) | arctan(1/3)-arctan(1/13)
arctan(1/5)+arctan(1/21) |
| arctan(1/5) | arctan(1/3)-arctan(1/8)
arctan(1/4)-arctan(1/21) arctan(1/6)+arctan(1/31) arctan(1/7)+arctan(1/18) |
| arctan(1/6) | arctan(1/5)-arctan(1/31)
arctan(1/7)+arctan(1/43) |
| arctan(1/7) | arctan(1/2)-arctan(1/3)
arctan(1/5)-arctan(1/18) arctan(1/6)-arctan(1/43) arctan(1/8)+arctan(1/57) arctan(1/9)+arctan(1/32) arctan(1/12)+arctan(1/17) |
| arctan(1/8) | arctan(1/3)-arctan(1/5)
arctan(1/7)-arctan(1/57) arctan(1/9)+arctan(1/73) arctan(1/13)+arctan(1/21) |
| arctan(1/9) | arctan(1/7)-arctan(1/32)
arctan(1/8)-arctan(1/73) arctan(1/10)+arctan(1/91) arctan(1/11)+arctan(1/50) |
| arctan(1/10) | arctan(1/9)-arctan(1/91)
arctan(1/11)+arctan(1/111) |
| arctan(1/11) | arctan(1/9)-arctan(1/50)
arctan(1/10)-arctan(1/111) arctan(1/12)+arctan(1/133) arctan(1/13)+arctan(1/72) |
| arctan(1/12) | arctan(1/7)-arctan(1/17)
arctan(1/11)-arctan(1/133) arctan(1/13)+arctan(1/157) arctan(1/17)+arctan(1/41) |
| arctan(1/13) | arctan(1/3)-arctan(1/4)
arctan(1/8)-arctan(1/21) arctan(1/11)-arctan(1/72) arctan(1/12)-arctan(1/157) arctan(1/14)+arctan(1/183) arctan(1/15)+arctan(1/98) arctan(1/18)+arctan(1/47) arctan(1/23)+arctan(1/30) |
| arctan(1/14) | arctan(1/13)-arctan(1/183)
arctan(1/15)+arctan(1/211) |
| arctan(1/15) | arctan(1/13)-arctan(1/98)
arctan(1/14)-arctan(1/211) arctan(1/16)+arctan(1/241) arctan(1/17)+arctan(1/128) |
| arctan(1/16) | arctan(1/15)-arctan(1/241)
arctan(1/17)+arctan(1/273) |
| arctan(1/17) | arctan(1/7)-arctan(1/12)
arctan(1/12)-arctan(1/41) arctan(1/15)-arctan(1/128) arctan(1/16)-arctan(1/273) arctan(1/18)+arctan(1/307) arctan(1/19)+arctan(1/162) arctan(1/22)+arctan(1/75) arctan(1/27)+arctan(1/46) |
| arctan(1/18) | arctan(1/5)-arctan(1/7)
arctan(1/13)-arctan(1/47) arctan(1/17)-arctan(1/307) arctan(1/19)+arctan(1/343) arctan(1/23)+arctan(1/83) arctan(1/31)+arctan(1/43) |
| arctan(1/19) | arctan(1/17)-arctan(1/162)
arctan(1/18)-arctan(1/343) arctan(1/20)+arctan(1/381) arctan(1/21)+arctan(1/200) |
| arctan(1/20) | arctan(1/19)-arctan(1/381)
arctan(1/21)+arctan(1/421) |
| arctan(1/21) | arctan(1/4)-arctan(1/5)
arctan(1/8)-arctan(1/13) arctan(1/19)-arctan(1/200) arctan(1/20)-arctan(1/421) arctan(1/22)+arctan(1/463) arctan(1/23)+arctan(1/242) arctan(1/34)+arctan(1/55) arctan(1/38)+arctan(1/47) |
| arctan(1/22) | arctan(1/17)-arctan(1/75)
arctan(1/21)-arctan(1/463) arctan(1/23)+arctan(1/507) arctan(1/27)+arctan(1/119) |
| arctan(1/23) | arctan(1/13)-arctan(1/30)
arctan(1/18)-arctan(1/83) arctan(1/21)-arctan(1/242) arctan(1/22)-arctan(1/507) arctan(1/24)+arctan(1/553) arctan(1/25)+arctan(1/288) arctan(1/28)+arctan(1/129) arctan(1/33)+arctan(1/76) |
| arctan(1/24) | arctan(1/23)-arctan(1/553)
arctan(1/25)+arctan(1/601) |
| arctan(1/25) | arctan(1/23)-arctan(1/288)
arctan(1/24)-arctan(1/601) arctan(1/26)+arctan(1/651) arctan(1/27)+arctan(1/338) |
| arctan(1/26) | arctan(1/25)-arctan(1/651)
arctan(1/27)+arctan(1/703) |
| arctan(1/27) | arctan(1/17)-arctan(1/46)
arctan(1/22)-arctan(1/119) arctan(1/25)-arctan(1/338) arctan(1/26)-arctan(1/703) arctan(1/28)+arctan(1/757) arctan(1/29)+arctan(1/392) arctan(1/32)+arctan(1/173) arctan(1/37)+arctan(1/100) |
| arctan(1/28) | arctan(1/23)-arctan(1/129)
arctan(1/27)-arctan(1/757) arctan(1/29)+arctan(1/813) arctan(1/33)+arctan(1/185) |
| arctan(1/29) | arctan(1/27)-arctan(1/392)
arctan(1/28)-arctan(1/813) arctan(1/30)+arctan(1/871) arctan(1/31)+arctan(1/450) |
| arctan(1/30) | arctan(1/13)-arctan(1/23)
arctan(1/29)-arctan(1/871) arctan(1/31)+arctan(1/931) arctan(1/47)+arctan(1/83) |
| arctan(1/31) | arctan(1/5)-arctan(1/6)
arctan(1/18)-arctan(1/43) arctan(1/29)-arctan(1/450) arctan(1/30)-arctan(1/931) arctan(1/32)+arctan(1/993) arctan(1/33)+arctan(1/512) arctan(1/44)+arctan(1/105) arctan(1/57)+arctan(1/68) |
| arctan(1/32) | arctan(1/7)-arctan(1/9)
arctan(1/27)-arctan(1/173) arctan(1/31)-arctan(1/993) arctan(1/33)+arctan(1/1057) arctan(1/37)+arctan(1/237) arctan(1/57)+arctan(1/73) |
| arctan(1/33) | arctan(1/23)-arctan(1/76)
arctan(1/28)-arctan(1/185) arctan(1/31)-arctan(1/512) arctan(1/32)-arctan(1/1057) arctan(1/34)+arctan(1/1123) arctan(1/35)+arctan(1/578) arctan(1/38)+arctan(1/251) arctan(1/43)+arctan(1/142) |
| arctan(1/34) | arctan(1/21)-arctan(1/55)
arctan(1/33)-arctan(1/1123) arctan(1/35)+arctan(1/1191) arctan(1/47)+arctan(1/123) |
| arctan(1/35) | arctan(1/33)-arctan(1/578)
arctan(1/34)-arctan(1/1191) arctan(1/36)+arctan(1/1261) arctan(1/37)+arctan(1/648) |
| arctan(1/36) | arctan(1/35)-arctan(1/1261)
arctan(1/37)+arctan(1/1333) |
| arctan(1/37) | arctan(1/27)-arctan(1/100)
arctan(1/32)-arctan(1/237) arctan(1/35)-arctan(1/648) arctan(1/36)-arctan(1/1333) arctan(1/38)+arctan(1/1407) arctan(1/39)+arctan(1/722) arctan(1/42)+arctan(1/311) arctan(1/47)+arctan(1/174) |
| arctan(1/38) | arctan(1/21)-arctan(1/47)
arctan(1/33)-arctan(1/251) arctan(1/37)-arctan(1/1407) arctan(1/39)+arctan(1/1483) arctan(1/43)+arctan(1/327) arctan(1/55)+arctan(1/123) |
| arctan(1/39) | arctan(1/37)-arctan(1/722)
arctan(1/38)-arctan(1/1483) arctan(1/40)+arctan(1/1561) arctan(1/41)+arctan(1/800) |
| arctan(1/40) | arctan(1/39)-arctan(1/1561)
arctan(1/41)+arctan(1/1641) |
| arctan(1/41) | arctan(1/12)-arctan(1/17)
arctan(1/39)-arctan(1/800) arctan(1/40)-arctan(1/1641) arctan(1/42)+arctan(1/1723) arctan(1/43)+arctan(1/882) arctan(1/70)+arctan(1/99) |
| arctan(1/42) | arctan(1/37)-arctan(1/311)
arctan(1/41)-arctan(1/1723) arctan(1/43)+arctan(1/1807) arctan(1/47)+arctan(1/395) |
| arctan(1/43) | arctan(1/6)-arctan(1/7)
arctan(1/18)-arctan(1/31) arctan(1/33)-arctan(1/142) arctan(1/38)-arctan(1/327) arctan(1/41)-arctan(1/882) arctan(1/42)-arctan(1/1807) arctan(1/44)+arctan(1/1893) arctan(1/45)+arctan(1/968) arctan(1/48)+arctan(1/413) arctan(1/53)+arctan(1/228) arctan(1/68)+arctan(1/117) arctan(1/80)+arctan(1/93) |
| arctan(1/44) | arctan(1/31)-arctan(1/105)
arctan(1/43)-arctan(1/1893) arctan(1/45)+arctan(1/1981) arctan(1/57)+arctan(1/193) |
| arctan(1/45) | arctan(1/43)-arctan(1/968)
arctan(1/44)-arctan(1/1981) arctan(1/46)+arctan(1/2071) arctan(1/47)+arctan(1/1058) |
| arctan(1/46) | arctan(1/17)-arctan(1/27)
arctan(1/45)-arctan(1/2071) arctan(1/47)+arctan(1/2163) arctan(1/75)+arctan(1/119) |
| arctan(1/47) | arctan(1/13)-arctan(1/18)
arctan(1/21)-arctan(1/38) arctan(1/30)-arctan(1/83) arctan(1/34)-arctan(1/123) arctan(1/37)-arctan(1/174) arctan(1/42)-arctan(1/395) arctan(1/45)-arctan(1/1058) arctan(1/46)-arctan(1/2163) arctan(1/48)+arctan(1/2257) arctan(1/49)+arctan(1/1152) arctan(1/52)+arctan(1/489) arctan(1/57)+arctan(1/268) arctan(1/60)+arctan(1/217) arctan(1/64)+arctan(1/177) arctan(1/73)+arctan(1/132) arctan(1/81)+arctan(1/112) |
| arctan(1/48) | arctan(1/43)-arctan(1/413)
arctan(1/47)-arctan(1/2257) arctan(1/49)+arctan(1/2353) arctan(1/53)+arctan(1/509) |
| arctan(1/49) | arctan(1/47)-arctan(1/1152)
arctan(1/48)-arctan(1/2353) arctan(1/50)+arctan(1/2451) arctan(1/51)+arctan(1/1250) |
| arctan(1/50) | arctan(1/9)-arctan(1/11)
arctan(1/49)-arctan(1/2451) arctan(1/51)+arctan(1/2551) arctan(1/91)+arctan(1/111) |
| arctan(1/51) | arctan(1/49)-arctan(1/1250)
arctan(1/50)-arctan(1/2551) arctan(1/52)+arctan(1/2653) arctan(1/53)+arctan(1/1352) |
| arctan(1/52) | arctan(1/47)-arctan(1/489)
arctan(1/51)-arctan(1/2653) arctan(1/53)+arctan(1/2757) arctan(1/57)+arctan(1/593) |
| arctan(1/53) | arctan(1/43)-arctan(1/228)
arctan(1/48)-arctan(1/509) arctan(1/51)-arctan(1/1352) arctan(1/52)-arctan(1/2757) arctan(1/54)+arctan(1/2863) arctan(1/55)+arctan(1/1458) arctan(1/58)+arctan(1/615) arctan(1/63)+arctan(1/334) |
| arctan(1/54) | arctan(1/53)-arctan(1/2863)
arctan(1/55)+arctan(1/2971) |
| arctan(1/55) | arctan(1/21)-arctan(1/34)
arctan(1/38)-arctan(1/123) arctan(1/53)-arctan(1/1458) arctan(1/54)-arctan(1/2971) arctan(1/56)+arctan(1/3081) arctan(1/57)+arctan(1/1568) arctan(1/72)+arctan(1/233) arctan(1/89)+arctan(1/144) |
| arctan(1/56) | arctan(1/55)-arctan(1/3081)
arctan(1/57)+arctan(1/3193) |
| arctan(1/57) | arctan(1/7)-arctan(1/8)
arctan(1/31)-arctan(1/68) arctan(1/32)-arctan(1/73) arctan(1/44)-arctan(1/193) arctan(1/47)-arctan(1/268) arctan(1/52)-arctan(1/593) arctan(1/55)-arctan(1/1568) arctan(1/56)-arctan(1/3193) arctan(1/58)+arctan(1/3307) arctan(1/59)+arctan(1/1682) arctan(1/62)+arctan(1/707) arctan(1/67)+arctan(1/382) arctan(1/70)+arctan(1/307) arctan(1/82)+arctan(1/187) arctan(1/83)+arctan(1/182) arctan(1/107)+arctan(1/122) |
| arctan(1/58) | arctan(1/53)-arctan(1/615)
arctan(1/57)-arctan(1/3307) arctan(1/59)+arctan(1/3423) arctan(1/63)+arctan(1/731) |
| arctan(1/59) | arctan(1/57)-arctan(1/1682)
arctan(1/58)-arctan(1/3423) arctan(1/60)+arctan(1/3541) arctan(1/61)+arctan(1/1800) |
| arctan(1/60) | arctan(1/47)-arctan(1/217)
arctan(1/59)-arctan(1/3541) arctan(1/61)+arctan(1/3661) arctan(1/73)+arctan(1/337) |
| arctan(1/61) | arctan(1/59)-arctan(1/1800)
arctan(1/60)-arctan(1/3661) arctan(1/62)+arctan(1/3783) arctan(1/63)+arctan(1/1922) |
| arctan(1/62) | arctan(1/57)-arctan(1/707)
arctan(1/61)-arctan(1/3783) arctan(1/63)+arctan(1/3907) arctan(1/67)+arctan(1/831) |
| arctan(1/63) | arctan(1/53)-arctan(1/334)
arctan(1/58)-arctan(1/731) arctan(1/61)-arctan(1/1922) arctan(1/62)-arctan(1/3907) arctan(1/64)+arctan(1/4033) arctan(1/65)+arctan(1/2048) arctan(1/68)+arctan(1/857) arctan(1/73)+arctan(1/460) |
| arctan(1/64) | arctan(1/47)-arctan(1/177)
arctan(1/63)-arctan(1/4033) arctan(1/65)+arctan(1/4161) arctan(1/81)+arctan(1/305) |
| arctan(1/65) | arctan(1/63)-arctan(1/2048)
arctan(1/64)-arctan(1/4161) arctan(1/66)+arctan(1/4291) arctan(1/67)+arctan(1/2178) |
| arctan(1/66) | arctan(1/65)-arctan(1/4291)
arctan(1/67)+arctan(1/4423) |
| arctan(1/67) | arctan(1/57)-arctan(1/382)
arctan(1/62)-arctan(1/831) arctan(1/65)-arctan(1/2178) arctan(1/66)-arctan(1/4423) arctan(1/68)+arctan(1/4557) arctan(1/69)+arctan(1/2312) arctan(1/72)+arctan(1/965) arctan(1/77)+arctan(1/516) |
| arctan(1/68) | arctan(1/31)-arctan(1/57)
arctan(1/43)-arctan(1/117) arctan(1/63)-arctan(1/857) arctan(1/67)-arctan(1/4557) arctan(1/69)+arctan(1/4693) arctan(1/73)+arctan(1/993) arctan(1/93)+arctan(1/253) arctan(1/105)+arctan(1/193) |
| arctan(1/69) | arctan(1/67)-arctan(1/2312)
arctan(1/68)-arctan(1/4693) arctan(1/70)+arctan(1/4831) arctan(1/71)+arctan(1/2450) |
| arctan(1/70) | arctan(1/41)-arctan(1/99)
arctan(1/57)-arctan(1/307) arctan(1/69)-arctan(1/4831) arctan(1/71)+arctan(1/4971) arctan(1/83)+arctan(1/447) arctan(1/99)+arctan(1/239) |
| arctan(1/71) | arctan(1/69)-arctan(1/2450)
arctan(1/70)-arctan(1/4971) arctan(1/72)+arctan(1/5113) arctan(1/73)+arctan(1/2592) |
| arctan(1/72) | arctan(1/11)-arctan(1/13)
arctan(1/55)-arctan(1/233) arctan(1/67)-arctan(1/965) arctan(1/71)-arctan(1/5113) arctan(1/73)+arctan(1/5257) arctan(1/77)+arctan(1/1109) arctan(1/89)+arctan(1/377) arctan(1/133)+arctan(1/157) |
| arctan(1/73) | arctan(1/8)-arctan(1/9)
arctan(1/32)-arctan(1/57) arctan(1/47)-arctan(1/132) arctan(1/60)-arctan(1/337) arctan(1/63)-arctan(1/460) arctan(1/68)-arctan(1/993) arctan(1/71)-arctan(1/2592) arctan(1/72)-arctan(1/5257) arctan(1/74)+arctan(1/5403) arctan(1/75)+arctan(1/2738) arctan(1/78)+arctan(1/1139) arctan(1/83)+arctan(1/606) arctan(1/86)+arctan(1/483) arctan(1/99)+arctan(1/278) arctan(1/114)+arctan(1/203) arctan(1/138)+arctan(1/155) |
| arctan(1/74) | arctan(1/73)-arctan(1/5403)
arctan(1/75)+arctan(1/5551) |
| arctan(1/75) | arctan(1/17)-arctan(1/22)
arctan(1/46)-arctan(1/119) arctan(1/73)-arctan(1/2738) arctan(1/74)-arctan(1/5551) arctan(1/76)+arctan(1/5701) arctan(1/77)+arctan(1/2888) arctan(1/104)+arctan(1/269) arctan(1/133)+arctan(1/172) |
| arctan(1/76) | arctan(1/23)-arctan(1/33)
arctan(1/75)-arctan(1/5701) arctan(1/77)+arctan(1/5853) arctan(1/129)+arctan(1/185) |
| arctan(1/77) | arctan(1/67)-arctan(1/516)
arctan(1/72)-arctan(1/1109) arctan(1/75)-arctan(1/2888) arctan(1/76)-arctan(1/5853) arctan(1/78)+arctan(1/6007) arctan(1/79)+arctan(1/3042) arctan(1/82)+arctan(1/1263) arctan(1/87)+arctan(1/670) |
| arctan(1/78) | arctan(1/73)-arctan(1/1139)
arctan(1/77)-arctan(1/6007) arctan(1/79)+arctan(1/6163) arctan(1/83)+arctan(1/1295) |
| arctan(1/79) | arctan(1/77)-arctan(1/3042)
arctan(1/78)-arctan(1/6163) arctan(1/80)+arctan(1/6321) arctan(1/81)+arctan(1/3200) |
| arctan(1/80) | arctan(1/43)-arctan(1/93)
arctan(1/79)-arctan(1/6321) arctan(1/81)+arctan(1/6481) arctan(1/117)+arctan(1/253) |
| arctan(1/81) | arctan(1/47)-arctan(1/112)
arctan(1/64)-arctan(1/305) arctan(1/79)-arctan(1/3200) arctan(1/80)-arctan(1/6481) arctan(1/82)+arctan(1/6643) arctan(1/83)+arctan(1/3362) arctan(1/98)+arctan(1/467) arctan(1/115)+arctan(1/274) |
| arctan(1/82) | arctan(1/57)-arctan(1/187)
arctan(1/77)-arctan(1/1263) arctan(1/81)-arctan(1/6643) arctan(1/83)+arctan(1/6807) arctan(1/87)+arctan(1/1427) arctan(1/107)+arctan(1/351) |
| arctan(1/83) | arctan(1/18)-arctan(1/23)
arctan(1/30)-arctan(1/47) arctan(1/57)-arctan(1/182) arctan(1/70)-arctan(1/447) arctan(1/73)-arctan(1/606) arctan(1/78)-arctan(1/1295) arctan(1/81)-arctan(1/3362) arctan(1/82)-arctan(1/6807) arctan(1/84)+arctan(1/6973) arctan(1/85)+arctan(1/3528) arctan(1/88)+arctan(1/1461) arctan(1/93)+arctan(1/772) arctan(1/96)+arctan(1/613) arctan(1/109)+arctan(1/348) arctan(1/136)+arctan(1/213) arctan(1/148)+arctan(1/189) |
| arctan(1/84) | arctan(1/83)-arctan(1/6973)
arctan(1/85)+arctan(1/7141) |
| arctan(1/85) | arctan(1/83)-arctan(1/3528)
arctan(1/84)-arctan(1/7141) arctan(1/86)+arctan(1/7311) arctan(1/87)+arctan(1/3698) |
| arctan(1/86) | arctan(1/73)-arctan(1/483)
arctan(1/85)-arctan(1/7311) arctan(1/87)+arctan(1/7483) arctan(1/99)+arctan(1/655) |
| arctan(1/87) | arctan(1/77)-arctan(1/670)
arctan(1/82)-arctan(1/1427) arctan(1/85)-arctan(1/3698) arctan(1/86)-arctan(1/7483) arctan(1/88)+arctan(1/7657) arctan(1/89)+arctan(1/3872) arctan(1/92)+arctan(1/1601) arctan(1/97)+arctan(1/844) |
| arctan(1/88) | arctan(1/83)-arctan(1/1461)
arctan(1/87)-arctan(1/7657) arctan(1/89)+arctan(1/7833) arctan(1/93)+arctan(1/1637) |
| arctan(1/89) | arctan(1/55)-arctan(1/144)
arctan(1/72)-arctan(1/377) arctan(1/87)-arctan(1/3872) arctan(1/88)-arctan(1/7833) arctan(1/90)+arctan(1/8011) arctan(1/91)+arctan(1/4050) arctan(1/106)+arctan(1/555) arctan(1/123)+arctan(1/322) |
| arctan(1/90) | arctan(1/89)-arctan(1/8011)
arctan(1/91)+arctan(1/8191) |
| arctan(1/91) | arctan(1/9)-arctan(1/10)
arctan(1/50)-arctan(1/111) arctan(1/89)-arctan(1/4050) arctan(1/90)-arctan(1/8191) arctan(1/92)+arctan(1/8373) arctan(1/93)+arctan(1/4232) arctan(1/132)+arctan(1/293) arctan(1/173)+arctan(1/192) |
| arctan(1/92) | arctan(1/87)-arctan(1/1601)
arctan(1/91)-arctan(1/8373) arctan(1/93)+arctan(1/8557) arctan(1/97)+arctan(1/1785) |
| arctan(1/93) | arctan(1/43)-arctan(1/80)
arctan(1/68)-arctan(1/253) arctan(1/83)-arctan(1/772) arctan(1/88)-arctan(1/1637) arctan(1/91)-arctan(1/4232) arctan(1/92)-arctan(1/8557) arctan(1/94)+arctan(1/8743) arctan(1/95)+arctan(1/4418) arctan(1/98)+arctan(1/1823) arctan(1/103)+arctan(1/958) arctan(1/118)+arctan(1/439) arctan(1/143)+arctan(1/266) |
| arctan(1/94) | arctan(1/93)-arctan(1/8743)
arctan(1/95)+arctan(1/8931) |
| arctan(1/95) | arctan(1/93)-arctan(1/4418)
arctan(1/94)-arctan(1/8931) arctan(1/96)+arctan(1/9121) arctan(1/97)+arctan(1/4608) |
| arctan(1/96) | arctan(1/83)-arctan(1/613)
arctan(1/95)-arctan(1/9121) arctan(1/97)+arctan(1/9313) arctan(1/109)+arctan(1/805) |
| arctan(1/97) | arctan(1/87)-arctan(1/844)
arctan(1/92)-arctan(1/1785) arctan(1/95)-arctan(1/4608) arctan(1/96)-arctan(1/9313) arctan(1/98)+arctan(1/9507) arctan(1/99)+arctan(1/4802) arctan(1/102)+arctan(1/1979) arctan(1/107)+arctan(1/1038) |
| arctan(1/98) | arctan(1/13)-arctan(1/15)
arctan(1/81)-arctan(1/467) arctan(1/93)-arctan(1/1823) arctan(1/97)-arctan(1/9507) arctan(1/99)+arctan(1/9703) arctan(1/103)+arctan(1/2019) arctan(1/115)+arctan(1/663) arctan(1/183)+arctan(1/211) |
| arctan(1/99) | arctan(1/41)-arctan(1/70)
arctan(1/70)-arctan(1/239) arctan(1/73)-arctan(1/278) arctan(1/86)-arctan(1/655) arctan(1/97)-arctan(1/4802) arctan(1/98)-arctan(1/9703) arctan(1/100)+arctan(1/9901) arctan(1/101)+arctan(1/5000) arctan(1/112)+arctan(1/853) arctan(1/125)+arctan(1/476) arctan(1/128)+arctan(1/437) arctan(1/157)+arctan(1/268) |
| arctan(1/100) | arctan(1/27)-arctan(1/37)
arctan(1/99)-arctan(1/9901) arctan(1/101)+arctan(1/10101) arctan(1/173)+arctan(1/237) |