Whipple 3F2 sum
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1: 34.2 Definition: Symbol
§34.2 Definition: Symbol
… βΊThe corresponding projective quantum numbers are given by … βΊWhen both conditions are satisfied the symbol can be expressed as the finite sum … βΊwhere is defined as in §16.2. βΊFor alternative expressions for the symbol, written either as a finite sum or as other terminating generalized hypergeometric series of unit argument, see Varshalovich et al. (1988, §§8.21, 8.24–8.26).2: 14.19 Toroidal (or Ring) Functions
§14.19(iv) Sums
… βΊ§14.19(v) Whipple’s Formula for Toroidal Functions
…3: 16.4 Argument Unity
Lerch Sum
… βΊWatson’s Sum
… βΊWhipple’s Sum
… βΊDΕΎrbasjan’s Sum
… βΊA different type of transformation is that of Whipple: …4: 16.6 Transformations of Variable
5: Bibliography W
6: 17.9 Further Transformations of Functions
§17.9(ii)
βΊTransformations of -Series
… βΊSears’ Balanced Transformations
… βΊWatson’s -Analog of Whipple’s Theorem
… βΊ§17.9(iv) Bibasic Series
…7: 17.7 Special Cases of Higher Functions
-Analog of Dixon’s Sum
… βΊGasper–Rahman -Analog of Watson’s Sum
… βΊGasper–Rahman -Analog of Whipple’s Sum
… βΊAndrews’ -Analog of the Terminating Version of Whipple’s Sum (16.4.7)
… βΊSecond -Analog of Bailey’s Sum
…8: 14.9 Connection Formulas
§14.9(iv) Whipple’s Formula
…9: Bibliography M
10: Errata
This equation was updated to include the value of the sum in terms of the function. Also the constraint was previously , .
The title of the paragraph which was previously “Andrews’ Terminating -Analog of (17.7.8)” has been changed to “Andrews’ -Analog of the Terminating Version of Watson’s Sum (16.4.6)”. The title of the paragraph which was previously “Andrews’ Terminating -Analog” has been changed to “Andrews’ -Analog of the Terminating Version of Whipple’s Sum (16.4.7)”.
Originally all the functions , , and in Equations (22.9.8), (22.9.9) and (22.9.10) were written incorrectly with . These functions have been corrected so that they are written with . In the sentence just below (22.9.10), the expression has been corrected to read .
Reported by Juan Miguel Nieto on 2019-11-07
In the original equation the prefactor of the above 3j symbol read . It is now replaced by its correct value .
Reported 2014-06-12 by James Zibin.
Originally the factor was missing in this equation.
Reported 2012-12-31 by Yu Lin.