### Abstract

A new non-polar spherical co-ordinate system for the three-dimensional space is introduced. The co-ordinate system is composed of six local co-ordinate systems mapped from six faces of a cube on to the 2-sphere. Weakly orthogonal and orthogonal spherical harmonics are constructed in this coordinate system. The spherical harmonics are easily computable functions consisting of polynomials and square root of polynomials. Examples of finite Fourier series computations are given in terms of the new spherical harmonics to demonstrate their immediate applicability.

Original language | English |
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Pages (from-to) | 1843-1854 |

Number of pages | 12 |

Journal | Mathematical Methods in the Applied Sciences |

Volume | 30 |

Issue number | 14 |

DOIs | |

Publication status | Published - Sep 25 2007 |

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### Keywords

- Curvilinear co-ordinate systems
- Fourier series on 2-sphere
- Laplace-Beltrami operator
- Spherical harmonics

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

**Spherical harmonics in a non-polar co-ordinate system and application to Fourier series in 2-sphere.** / Nasir, H. M.

Research output: Contribution to journal › Article

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TY - JOUR

T1 - Spherical harmonics in a non-polar co-ordinate system and application to Fourier series in 2-sphere

AU - Nasir, H. M.

PY - 2007/9/25

Y1 - 2007/9/25

N2 - A new non-polar spherical co-ordinate system for the three-dimensional space is introduced. The co-ordinate system is composed of six local co-ordinate systems mapped from six faces of a cube on to the 2-sphere. Weakly orthogonal and orthogonal spherical harmonics are constructed in this coordinate system. The spherical harmonics are easily computable functions consisting of polynomials and square root of polynomials. Examples of finite Fourier series computations are given in terms of the new spherical harmonics to demonstrate their immediate applicability.

AB - A new non-polar spherical co-ordinate system for the three-dimensional space is introduced. The co-ordinate system is composed of six local co-ordinate systems mapped from six faces of a cube on to the 2-sphere. Weakly orthogonal and orthogonal spherical harmonics are constructed in this coordinate system. The spherical harmonics are easily computable functions consisting of polynomials and square root of polynomials. Examples of finite Fourier series computations are given in terms of the new spherical harmonics to demonstrate their immediate applicability.

KW - Curvilinear co-ordinate systems

KW - Fourier series on 2-sphere

KW - Laplace-Beltrami operator

KW - Spherical harmonics

UR - http://www.scopus.com/inward/record.url?scp=34548458052&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34548458052&partnerID=8YFLogxK

U2 - 10.1002/mma.872

DO - 10.1002/mma.872

M3 - Article

VL - 30

SP - 1843

EP - 1854

JO - Mathematical Methods in the Applied Sciences

JF - Mathematical Methods in the Applied Sciences

SN - 0170-4214

IS - 14

ER -