Difference between revisions of "User:Tohline/Math/EQ Q1minusHalf01"

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[[Image:LSU_Key.png|25px|link=http://www.vistrails.org/index.php/User:Tohline/Appendix/Equation_templates#Special_Function_Relationships]]
[[Image:LSU_Key.png|25px|link=http://www.vistrails.org/index.php/User:Tohline/Appendix/Equation_templates#Toroidal_Function_Evaluations]]
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[https://books.google.com/books?id=MtU8uP7XMvoC&printsec=frontcover&dq=Abramowitz+and+stegun&hl=en&sa=X&ved=0ahUKEwialra5xNbaAhWKna0KHcLAASAQ6AEILDAA#v=onepage&q=Abramowitz%20and%20stegun&f=false Abramowitz &amp; Stegun (1995)], p. 337, eq. (8.13.7)
where: &nbsp; <math>~k = \sqrt{ \frac{2}{z+1}} \, .</math>
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(see our [[User:Tohline/Appendix/Mathematics/ToroidalSynopsis01#Evaluating_Q2.CE.BD|associated derivation]])
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Latest revision as of 21:43, 1 July 2018

LSU Key.png

<math>~Q^1_{-\frac{1}{2}}(z)</math>

<math>~=</math>

<math>~ - \biggl[\frac{1}{2(z-1)} \biggr]^{1 / 2} E(k) </math>

where:   <math>~k = \sqrt{ \frac{2}{z+1}} \, .</math>

(see our associated derivation)