Menu
Home
People
Places
Arts
History
Plants & Animals
Science
Life & Culture
Technology
Reference.org
Quaternionic analysis
open-in-new
<p>In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, quaternionic analysis is the study of <a href="/facts/Function_(mathematics)/CdReEKCh">functions</a> with <a href="/facts/Quaternion/T3tnu7mX">quaternions</a> as the <a href="/facts/Domain_of_a_function/FQvoeUpX">domain</a> and/or range. Such functions can be called functions of a quaternion variable just as <a href="/facts/Function_of_a_real_variable/bbNG3DnN">functions of a real variable</a> or a <a href="/facts/Function_of_a_complex_variable/hgCoQlH0">complex variable</a> are called. </p><p>As with <a href="/facts/Complex_analysis/hgCoQlH0">complex</a> and <a href="/facts/Real_analysis/12WjlXCW">real analysis</a>, it is possible to study the concepts of <a href="/facts/Analytic_function/JhL3z8FP">analyticity</a>, <a href="/facts/Holomorphic_function/kVzthtEf">holomorphy</a>, <a href="/facts/Harmonic_function/H6pg4dMT">harmonicity</a> and <a href="/facts/Conformality/cEpQnMad">conformality</a> in the context of quaternions. Unlike the <a href="/facts/Complex_number/2w7mqI7e">complex numbers</a> and like the <a href="/facts/Real_number/R02gw5Pb">reals</a>, the four notions do not coincide. </p>