Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9805)

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=-17/4, b_1`>=-11/2

For fixed z and a₁=-17/4, b_1`=-7/2

http://functions.wolfram.com/07.22.03.9805.01

Input Form

HypergeometricPFQ[{-(17/4)}, {-(7/2), 11/4}, -z] == (1/(30198988800 z^(7/4))) (Sqrt[Pi] (-6230890575 - 9494690400 z + 22340448000 z^2 - 7332249600 z^3 + 1086259200 z^4 - 106954752 z^5 + 16777216 z^6) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) (4 Sqrt[z] (-2076963525 + 1559445840 z - 476398080 z^2 + 69574656 z^3 - 6881280 z^4 + 1048576 z^5) Cos[2 Sqrt[z]] + (6230890575 + 2848407120 z - 581184000 z^2 + 78028800 z^3 - 7667712 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]