erfi, erfw (w(z)) functions
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09-03-2021, 10:39 AM
Post: #3
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RE: erfi, erfw (w(z)) functions
For odd functions (erf ↔ erfi, sin ↔ sinh, tan ↔ tanh, and their inverse), we can swap the parts.
Let swap(x + y*i) = y + x*i sinh(z) = swap(sin(swap(z))) sin(z) = swap(sinh(swap(z))) ... >>> from cmath import * >>> sin(3+4j) (3.8537380379193773-27.016813258003932j) >>> sinh(4+3j) (-27.016813258003932+3.8537380379193773j) This is easier to remember, without worrying signs of ×/÷ i Code is likely simpler, since ×/÷ i is usually implemented by swap parts, then fix sign. From HP-71B cpr.a, http://www.jeffcalc.hp41.eu/emu71/mathrom.html Code: * ************************ Proof is trivial, since swap(z) = i*conj(z) sinh(z) = sin(i*z) / i conj(sinh(z)) = sinh(conj(z)) = sin(i*conj(z)) / i Multiply-by-i, and replace i*conj() by swap() swap(sinh(z)) = sin(swap(z)) |
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erfi, erfw (w(z)) functions - salvomic - 11-01-2017, 06:03 PM
RE: erfi, erfw (w(z)) functions - Albert Chan - 08-22-2020, 04:10 PM
RE: erfi, erfw (w(z)) functions - Albert Chan - 09-03-2021 10:39 AM
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