Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9013)

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`=9/2

http://functions.wolfram.com/07.22.03.9013.01

Input Form

HypergeometricPFQ[{-(21/4)}, {9/2, -(13/4)}, -z] == (2 Sqrt[z] (-128074828006125 + 18974048593500 z - 2639867630400 z^2 + 213794380800 z^3 - 22992076800 z^4 + 4376494080 z^5 - 2202009600 z^6 + 12280922112 z^7 + 268435456 z^8) Cos[2 Sqrt[z]] + 67108864 Sqrt[Pi] z^(31/4) (735 + 16 z) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + (128074828006125 - 189740485935000 z - 17599117536000 z^2 + 1482030950400 z^3 - 132843110400 z^4 + 18331729920 z^5 - 5284823040 z^6 + 6039797760 z^7 + 134217728 z^8) Sin[2 Sqrt[z]])/ (31634044041600 z^(7/2))

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]