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Write an exponential of a symbolic multiple of i arctan as powers of the linears - #1934
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Rafael-SOWNet merged 3 commits intoOct 18, 2026
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…the linears e^(k i arctan(L)) is (1 + i L)^(k/2) (1 - i L)^(-k/2) and (K (1 + L^2))^q is K^q (1 + i L)^q (1 - i L)^q, both exactly for a real L and any k and q. (c + a^2 c x^2)^p/e^(2 i p arctan(a x)) is then c^p (1 - i a x)^(2p), a power of a linear; it was left unevaluated (Rubi's 5.3.6:502 and :503). Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura
…-of-an-arctangent-in-an-exponential
…G-CHANGES Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura
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For a real
L,e^(k i arctan(L))is(1 + i L)^(k/2) (1 - i L)^(-k/2), and(K (1 + L²))^qisK^q (1 + i L)^q (1 - i L)^q, for anykandq. An exponential of a symbolic multiple ofi arctan(L)beside powers of multiples of1 + L²is written so, with the exponents simplified, and becomes a product of powers of the two linears.(c + a² c x²)^p/e^(2 i p arctan(a x))isc^p (1 - i a x)^(2p), a power of a linear; it was left unevaluated.Part of #718 — Rubi's 5.3.6:502 and :503.
Measured against master b2ef509:
Recorded in BREAKING-CHANGES.md.
🤖 Generated with Claude Code
https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura