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Date: 10-5-2018
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Date: 9-9-2019
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Date: 18-8-2018
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The central beta function is defined by
(1) |
where is the beta function. It satisfies the identities
(2) |
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(3) |
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(4) |
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(5) |
With , the latter gives the Wallis formula. For , 2, ... the first few values are 1, 1/6, 1/30, 1/140, 1/630, 1/2772, ... (OEIS A002457), which have denominators .
When ,
(6) |
where
(7) |
The central beta function satisfies
(8) |
(9) |
(10) |
(11) |
For an odd positive integer, the central beta function satisfies the identity
(12) |
REFERENCES:
Borwein, J. M. and Zucker, I. J. "Elliptic Integral Evaluation of the Gamma Function at Rational Values of Small Denominators." IMA J. Numerical Analysis 12, 519-526, 1992.
Sloane, N. J. A. Sequence A002457/M4198 in "The On-Line Encyclopedia of Integer Sequences."
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هل يمكن للدماغ البشري التنبؤ بالمستقبل أثناء النوم؟
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علماء: طول الأيام على الأرض يزداد بسبب النواة الداخلية
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المجمع العلمي يشرك طلبة الدورات الصيفية بمحفلٍ قرآني في محافظة بابل
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