Hypergeometric function – Perimeter of an Ellipse and other applications (wp34s)

01162020, 04:18 AM
(This post was last modified: 01162020 04:19 AM by Gerson W. Barbosa.)
Post: #10




RE: Hypergeometric function – Perimeter of an Ellipse and other applications (wp34s)
(01142020 11:47 PM)Albert Chan Wrote: BTW, if you change "⅗" to "217/360", above formula is always better than Ramanujan II Except at the vicinity of h = 1, when Ramanujan II becomes better, albeit only slightly. Here are the fixed expression for s and the new HP42S/Free42 version: s = 3/2 + h²/[32  h²(217h²/360 + 4)] 00 { 66Byte Prgm } 01▸LBL "MB" 02 COMPLEX 03 ENTER 04 COMPLEX 05 ENTER 06 X<> ST Z 07 STO ST Z 08 + 09 ÷ 10 X↑2 11 0.361 12 →HR 13 RCL× ST Y 14 4 15 + 16 RCL× ST Y 17 +/ 18 32 19 + 20 ÷ 21 1.5 22 + 23 X<>Y 24 COMPLEX 25 RCL ST Z 26 Y↑X 27 X<>Y 28 LASTX 29 Y↑X 30 + 31 2 32 ÷ 33 X<>Y 34 1/X 35 Y↑X 36 STO+ ST X 37 PI 38 × 39 END The error when computing the length of Halley’s comet is now 1146.924 km, about the flight distance from Milan to Warsaw („Z ziemi włoskiej do Polski”), but the results are overall better. 

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