Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8945)

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=-21/4, b_1`>=-11/2

For fixed z and a₁=-21/4, b_1`=5/2

http://functions.wolfram.com/07.22.03.8945.01

Input Form

HypergeometricPFQ[{-(21/4)}, {5/2, 15/4}, -z] == (Sqrt[Pi] (-179304759208575 - 3278715596956800 z + 20400897047731200 z^2 + 93261243646771200 z^3 + 33913179507916800 z^4 + 3215471834824704 z^5 + 104144836755456 z^6 + 1217623228416 z^7 + 4294967296 z^8) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) (4 Sqrt[z] (-59768253069525 + 700351619451120 z + 5499502780665600 z^2 + 2084377306411008 z^3 + 199777074610176 z^4 + 6494893375488 z^5 + 76051120128 z^6 + 268435456 z^7) Cos[2 Sqrt[z]] + (179304759208575 - 444411189789840 z + 4405326895307520 z^2 + 1952825133772800 z^3 + 195136818315264 z^4 + 6438698090496 z^5 + 75849793536 z^6 + 268435456 z^7) Sin[2 Sqrt[z]]))/ (79815202622668800 z^(11/4))

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]