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3 F 4 Hypergeometric Functions as a Sum of a Product of 1 F 2 Functions

Author

Listed:
  • Jack C. Straton

    (Department of Physics, Portland State University, Portland, OR 97207-0751, USA)

Abstract

This paper shows that certain F 4 3 hypergeometric functions can be expanded in sums of pair products of F 2 1 functions. In special cases, the F 4 3 hypergeometric functions reduce to F 3 2 functions. Further special cases allow one to reduce the F 3 2 functions to F 2 1 functions, and the sums to products of F 1 0 (Bessel) and F 2 1 functions. The class of hypergeometric functions with summation theorems are thereby expanded beyond those expressible as pair-products of F 1 2 functions, F 2 3 functions, and generalized Whittaker functions, into the realm of F q p functions where p < q for both the summand and terms in the series.

Suggested Citation

  • Jack C. Straton, 2025. "3 F 4 Hypergeometric Functions as a Sum of a Product of 1 F 2 Functions," Mathematics, MDPI, vol. 13(3), pages 1-12, January.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:3:p:421-:d:1578402
    as

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