Tables of the complete and incomplete elliptic integrals: reissued from tome II of Legendre's Traité des fonctions elliptiques, Paris, 1825
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Incomplete Elliptic Integrals Use of Table II when modulus and amplitude both
Direct Determination of Incomplete Elliptic Integrals with high modulus
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84 terms accordingly Andoyer's Table angle and amplitude antilogarithm appropriate root back interpolate backward interpolation central difference formula circular measure coefficients corresponding cos2 cosec decimal place accuracy determining Diff differences will suffice direct interpolation eleventh decimal place elliptic functions equation fifteen decimal place fourth order differences given Hence Illustration includes third differences INCOMPLETE ELLIPTIC INTEGRALS interpolation formula interpolation into Andoyer's inverse interpolation KARL PEARSON laborious labour Legendre Legendre's Table linear interpolation Logarithmetica Britannica Logarithms of Numbers loge logF1 modular angle moduli method Multiplying Natural Sines nine figures ninth decimal place notation O.OOOOO obtain omit oo5o oooo ooooo quadratic for xi require second elliptic integral second order differences series of angles seventh decimal square root Table of Natural Tangent Tracts for Computers twelfth decimal place twelve decimal places twelve figures twenty figures unit wrong units in error unity value found xvii xviii zero