Almkvist-Giullera formula for pi: Difference between revisions
Content added Content deleted
m (→{{header|dc}}: Add output header) |
(→{{header|Common Lisp}}: Add output header.) |
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(defun integral (n) |
(defun integral (n) |
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(/r (*r 32 (!r (*r 6 n)) (+r (*r 532 n n) (*r 126 n) 9)) (*r 3 (expt-r (!r n) 6)))) |
(/r (*r 32 (!r (*r 6 n)) (+r (*r 532 n n) (*r 126 n) 9)) (*r 3 (expt-r (!r n) 6)))) |
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; the exponent for 10 in the nth term of the series |
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(defun power (n) (- 3 (* 6 (1+ n)))) |
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; the nth term of the series |
; the nth term of the series |
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(defun a-g (n) |
(defun a-g (n) |
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(/r (integral n) (expt-r 10 ( |
(/r (integral n) (expt-r 10 (abs (power n))))) |
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; the sum of the first n terms |
; the sum of the first n terms |
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(sqrt-r (/r 1 (a-g-sigma n)))) |
(sqrt-r (/r 1 (a-g-sigma n)))) |
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(format t "~A. ~44A~4A ~A~%" "N" "Integral part of Nth term" "×10^" "=Actual value of Nth term") |
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(loop for i from 0 to 9 doing |
(loop for i from 0 to 9 doing |
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(format t "~&~a. ~44d ~3d " i (integral i) ( |
(format t "~&~a. ~44d ~3d " i (integral i) (power i)) |
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(finish-output *standard-output*) |
(finish-output *standard-output*) |
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(print-r (a-g i) 50 nil)) |
(print-r (a-g i) 50 nil)) |
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{{Out}} |
{{Out}} |
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<pre> |
<pre>N. Integral part of Nth term ×10^ =Actual value of Nth term |
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0. 96 -3 +0.09600000000000000000000000000000000000000000000000... |
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1. 5122560 -9 +0.00512256000000000000000000000000000000000000000000... |
1. 5122560 -9 +0.00512256000000000000000000000000000000000000000000... |
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2. 190722470400 -15 +0.00019072247040000000000000000000000000000000000000... |
2. 190722470400 -15 +0.00019072247040000000000000000000000000000000000000... |
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