Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8403)

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=-23/4, b_1`>=-11/2

For fixed z and a₁=-23/4, b_1`=7/2

http://functions.wolfram.com/07.22.03.8403.01

Input Form

HypergeometricPFQ[{-(23/4)}, {7/2, 1/4}, -z] == (1/(639566928000 z^(5/2))) (Sqrt[Pi] z^(13/4) (4311055200375 + 2898188370000 z + 401480640000 z^2 + 17129840640 z^3 + 248709120 z^4 + 1048576 z^5) FresnelC[(2 z^(1/4))/Sqrt[Pi]] - 2 ((-Sqrt[z]) (-12265060500 - 21804552000 z + 164244326400 z^2 + 161086214025 z^3 + 24144056640 z^4 + 1056284160 z^5 + 15482880 z^6 + 65536 z^7) Cos[2 Sqrt[z]] + 2 (-3066265125 - 1362784500 z - 30526372800 z^2 + 486984960000 z^3 + 353667238650 z^4 + 49796017920 z^5 + 2135454720 z^6 + 31064064 z^7 + 131072 z^8) 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]