The Leibniz formula for &#x03C0;<!-- π --> <mrow class="MJX-TeXAtom-ORD"> / </mrow> 4

enrotlavaec

enrotlavaec

Answered question

2022-06-24

The Leibniz formula for π / 4 is:
i = 0 ( 1 ) i 2 i + 1 = 1 1 3 + 1 5 1 7 + . . .

Answer & Explanation

marktje28

marktje28

Beginner2022-06-25Added 22 answers

i = 0 n ( 1 ) i 2 i + 1 = ( 1 ) n 2 [ ψ 0 ( 3 / 2 + n ) ψ 0 ( 1 / 2 ) ] ,
where ψ 0 ( x ) is the Polygamma function (also known as the DiGamma function for this case). There are likely no further simplifications possible (if this even counts as one).

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