Search results for "Legend"

Fourier series for elliptic integrals and some generalizations via hypergeometric series

2008

Fourier series are derived for generalizations of the three canonical Legendre incomplete elliptic integrals using a hypergeometric series approach. The Fourier series for the incomplete Epstein–Hubbell integrals are obtained as special cases of the generalization of the Legendre integrals of the first and second kinds. The Fourier series for the integrals of the first and second kinds, and those for the Epstein–Hubbell integrals, were obtained recently using a different approach, but the series obtained for the generalization of the incomplete integral of the third kind is new. All cases of the integral of the third kind are given, with the modulus and the parameter being complex variables…

Indefinite integrals of incomplete elliptic integrals from Jacobi elliptic functions

2017

Integration formulas are derived for the three canonical Legendre elliptic integrals. These formulas are obtained from the differential equations satified by these elliptic integrals when the indep...

Indefinite integrals involving the Jacobi Zeta and Heuman Lambda functions

2017

ABSTRACTJacobian elliptic functions are used to obtain formulas for deriving indefinite integrals for the Jacobi Zeta function and Heuman's Lambda function. Only sample results are presented, mostly obtained from powers of the twelve Glaisher elliptic functions. However, this sample includes all such integrals in the literature, together with many new integrals. The method used is based on the differential equations obeyed by these functions when the independent variable is the argument u of elliptic function theory. The same method was used recently, in a companion paper, to derive similar integrals for the three canonical incomplete elliptic integrals.

La imatge dels Borja al cinema

2016

Resum: La imatge dels Borja com a paradigma de l’abús del poder, de l’ambició desmesurada, de l’avidesa pels diners, de la luxúria i de la corrupció moral, que arranca des de la seua més estricta contemporaneïtat, travessa més de cinc-cents anys afaiçonada pel gran volum de literatura que ha generat el llinatge, és recollida pel cinematògraf a finals del segle XIX. Aquest nou mitjà d’expressió, que ha aportat més de 80 produccions fílmiques, ha contribuït a magnificar la dimensió universal dels Borja i ha fixat una determinada visió en l’imaginari global. Abstract: The image of the Borgias as a paradigm of abuse of power, untampered ambition, greed for money, lust and moral corruption, whic…

Evaluation of legendre functions of argument greater than one

1997

Abstract In this paper we present an algorithm to evaluate Legendre functions of the first and second kinds ( P v , Q v ) for integraland half-integral order and argument greater than one. The code is based on the calculation of the continued fraction for the Q 's. the Wronskian relating P 's and Q 's and the application of forward recurrence relations for the P 's and backward recurrence for the Q 's. We also show an application of these algorithms to the evaluation of the electrostatic field due to a charged toroidal conductor at potential V .

A code to evaluate prolate and oblate spheroidal harmonics

1998

Abstract We present a code to evaluate prolate ( P n m ( x ), Q n m ( x ); n ≥ m , x > 1) and oblate ( P n m ( ix ), Q n m ( ix ); n ≥ m , x > 0) spheroidal harmonics, that is, spherical harmonics ( n and m integers) for real arguments larger than one and for purely imaginary arguments. We start from the known values (in closed form) of P m m and P m +1 m and we apply the forward recurrence relation over n up to a given degree n = N Max . The Wronskian relating P 's and Q 's, together with the evaluation of the continued fraction for Q m+N staggeredMax m / Q m+N staggeredMax -1 m , allows the calculation of Q m+N staggeredMax m and Q m+N staggeredMax -1 m . Backward recurrence is then appli…

Icarus and Daedalus in Toni Morrison's "Song of Solomon"

2012

In Song of Solomon Toni Morrison rewrites the legend of the Flying Africans and the Myth of Icarus to create her own Myth. Her depiction of the black hero’s search for identity has strong mythical overtones. Morrison rescues those elements of mythology black culture which are still relevant to blacks and fuses them with evident allusions to Greek mythology. She reinterprets old images and myths of flight, the main mythical motif in the story. Her Icarus engages on an archetypical journey to the South, to his family past, led by his Daedalic guide, on which he finally recovers his ancestral ability to fly. His flight signals a spiritual epiphany in the hero’s quest for self-definition in the…

In the beginning, this was an empty place... Place-related narratives in Timofeyevka, Siberia

2014

Reimagining cultural memory of the arctic in the graphic narratives of Oqaluttuaq

2021

The Greenlandic oral story-telling tradition, Oqaluttuaq, meaning “history,” “legend,” and “narrative,” is recognized as an important entry point into Arctic collective memory. The graphic artist Nuka K. Godtfredsen and his literary and scientific collaborators have used the term as the title of graphic narratives published from 2009 to 2018, and focused on four moments or ‘snippets’ from Greenland’s history (from the periods of Saqqaq, late Dorset, Norse settlement, and European colonization). Adopting a fragmentary and episodic approach to historical narrativization, the texts frame the modern European presence in Greenland as one of multiple migrations to and settlements in the Artic, ra…

Indefinite integrals of special functions from hybrid equations

2019

Elementary linear first and second order differential equations can always be constructed for twice differentiable functions by explicitly including the function's derivatives in the definition of ...