Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a9hx)

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=-9/4, b_1`>=-11/2

For fixed z and a₁=-9/4, b_1`=1/2

http://functions.wolfram.com/07.22.03.a9hx.01

Input Form

HypergeometricPFQ[{-(9/4)}, {1/2, 19/4}, -z] == (1/(6442450944 z^(15/4))) (11 (Sqrt[Pi] (-127702575 - 85730400 z - 54432000 z^2 - 77414400 z^3 + 928972800 z^4 + 396361728 z^5 + 16777216 z^6) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) (4 Sqrt[z] (-42567525 - 9117360 z - 8225280 z^2 + 53846016 z^3 + 24576000 z^4 + 1048576 z^5) Cos[2 Sqrt[z]] + (127702575 - 50485680 z - 2419200 z^2 + 38707200 z^3 + 23789568 z^4 + 1048576 z^5) 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]