Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8499)

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=-23/4, b_1`>=-11/2

For fixed z and a₁=-23/4, b_1`=11/2

http://functions.wolfram.com/07.22.03.8499.01

Input Form

HypergeometricPFQ[{-(23/4)}, {11/2, 1/4}, -z] == (2 Sqrt[z] (-23717560741875 - 531485955000 z - 1569927744000 z^2 - 3256146432000 z^3 + 12821874278400 z^4 + 7677416278800 z^5 + 815713213440 z^6 + 26867752960 z^7 + 308019200 z^8 + 1048576 z^9) Cos[2 Sqrt[z]] + 16 Sqrt[Pi] z^(21/4) (18318965655375 + 8374384299600 z + 840063628800 z^2 + 27153571840 z^3 + 309002240 z^4 + 1048576 z^5) FresnelC[(2 z^(1/4))/Sqrt[Pi]] - (-23717560741875 + 31091928367500 z + 7571630682000 z^2 + 2238600672000 z^3 - 11722127155200 z^4 + 136266537369600 z^5 + 65818062480000 z^6 + 6680771297280 z^7 + 216768512000 z^8 + 2470445056 z^9 + 8388608 z^10) Sin[2 Sqrt[z]])/ (61601462208000 z^(9/2))

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]