Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8027)

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`=-9/2

http://functions.wolfram.com/07.22.03.8027.01

Input Form

HypergeometricPFQ[{-(23/4)}, {-(9/2), 9/4}, -z] == (Sqrt[Pi] (2292816782025 + 11165020851600 z - 9402122822400 z^2 + 2387840716800 z^3 - 315747532800 z^4 + 28868345856 z^5 - 2701131776 z^6 - 268435456 z^7) FresnelC[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) ((-(2292816782025 + 728697180960 z - 171149287680 z^2 + 21495398400 z^3 - 1900609536 z^4 + 153092096 z^5 + 16777216 z^6)) Cos[2 Sqrt[z]] + 4 Sqrt[z] (-764272260675 + 623034205920 z - 153589766400 z^2 + 20099186688 z^3 - 1829044224 z^4 + 165675008 z^5 + 16777216 z^6) Sin[2 Sqrt[z]]))/(15981304872960 z^(5/4))

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]