Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8215)

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`=-1/2

http://functions.wolfram.com/07.22.03.8215.01

Input Form

HypergeometricPFQ[{-(23/4)}, {-(1/2), 5/4}, -z] == (1/(117315993600 z^(1/4))) ((-Sqrt[Pi]) (-45176306175 + 481880599200 z + 2753603424000 z^2 + 1068064358400 z^3 + 94939054080 z^4 + 2459959296 z^5 + 16777216 z^6) FresnelC[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) ((-(-13481690625 + 126900905040 z + 61724136960 z^2 + 5793423360 z^3 + 152764416 z^4 + 1048576 z^5)) Cos[2 Sqrt[z]] + 4 Sqrt[z] (14270229675 + 161659820880 z + 65701854720 z^2 + 5905293312 z^3 + 153550848 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]