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Evaluate the Epstein–Hubbell integral
ResourceFunction["EpsteinHubbellOmega"][n,m] gives the Epstein–Hubbell integral Ωn(m). |
Evaluate numerically:
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Plot Ω2(m):
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Series at the origin:
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Evaluate for complex arguments and orders:
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Evaluate to high precision:
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The precision of the output tracks the precision of the input:
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EpsteinHubbellOmega threads elementwise over lists:
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Log plot of a family of Epstein–Hubbell integrals:
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For integer n, EpsteinHubbellOmega can be expressed in terms of EllipticE and EllipticK:
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For integer n, EpsteinHubbellOmega can be expressed in terms of half-integer order LegendreP:
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For integer n, EpsteinHubbellOmega can be expressed in terms of LegendreQ:
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Express an Epstein–Hubbell integral of noninteger order in terms of simpler functions:
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Compare EpsteinHubbellOmega with the integral definition:
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