Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8b3)

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=-15/4, b_1`>=-11/2

For fixed z and a₁=-15/4, b_1`=9/2

http://functions.wolfram.com/07.22.03.a8b3.01

Input Form

HypergeometricPFQ[{-(15/4)}, {9/2, 13/4}, -z] == (1/(3024145612800 z^(7/2))) (Sqrt[Pi] z^(5/4) (524644745625 - 1119242124000 z + 3443821920000 z^2 + 1440552960000 z^3 + 117596160000 z^4 + 2736783360 z^5 + 16777216 z^6) FresnelC[(2 z^(1/4))/Sqrt[Pi]] - 2 ((-Sqrt[z]) (38320128000 - 105678012825 z + 152870533200 z^2 + 83740976640 z^3 + 7193272320 z^4 + 170065920 z^5 + 1048576 z^6) Cos[2 Sqrt[z]] + 4 (4790016000 + 45984153600 z - 87398405325 z^2 + 200970277200 z^3 + 88723975680 z^4 + 7318118400 z^5 + 170852352 z^6 + 1048576 z^7) 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]