Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8849)

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`=1/2

http://functions.wolfram.com/07.22.03.8849.01

Input Form

HypergeometricPFQ[{-(21/4)}, {1/2, 15/4}, -z] == (Sqrt[Pi] (-12993098493375 - 26398676304000 z - 98555058201600 z^2 + 3153761862451200 z^3 + 4205015816601600 z^4 + 854352419880960 z^5 + 47795939573760 z^6 + 856845975552 z^7 + 4294967296 z^8) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) (4 Sqrt[z] (-4331032831125 - 6819658045200 z + 163641329913600 z^2 + 253899177799680 z^3 + 52858201374720 z^4 + 2977315160064 z^5 + 53502541824 z^6 + 268435456 z^7) Cos[2 Sqrt[z]] + (12993098493375 + 12539371244400 z + 73916293651200 z^2 + 222155248250880 z^3 + 50785312112640 z^4 + 2938031308800 z^5 + 53301215232 z^6 + 268435456 z^7) Sin[2 Sqrt[z]]))/ (1542322755993600 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]