Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8av)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

For rational parameters with larger denominators and fixed z

For fixed z and a₁=-15/4, b_1`>=-11/2

For fixed z and a₁=-15/4, b_1`=9/2

http://functions.wolfram.com/07.22.03.a8av.01

Input Form

HypergeometricPFQ[{-(15/4)}, {9/2, 5/4}, -z] == (1/(1107475200 z^(7/2))) (Sqrt[Pi] z^(13/4) (896828625 + 1125432000 z + 183744000 z^2 + 7127040 z^3 + 65536 z^4) FresnelC[(2 z^(1/4))/Sqrt[Pi]] + 2 (Sqrt[z] (14033250 + 8731800 z + 19958400 z^2 + 61082415 z^3 + 11081520 z^4 + 441600 z^5 + 4096 z^6) Cos[2 Sqrt[z]] - (7016625 - 4989600 z + 1663200 z^2 + 186278400 z^3 + 273434220 z^4 + 45608640 z^5 + 1778688 z^6 + 16384 z^7) Sin[2 Sqrt[z]]))

Standard Form

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MathML Form

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Rule Form

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Date Added to functions.wolfram.com (modification date)

2007-05-02

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]